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We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full formalism of quantum mechanics in a generic curved space(time). Our basic perspective is to take seriously the noncommutative symplectic geometry corresponding to the quantum observable algebra. Particle position coordinate transformations and a nontrivial metric assigning an invariant inner product to vectors, and covectors, are implemented accordingly. That allows an analog to the classical picture of the phase space as the cotangent bundle. The mass-independent quantum geodesic equations as equations of free particle motion under a generic metric as a quantum observable are obtained from an invariant Hamiltonian. Hermiticity of momentum observables is to be taken as reference frame dependent. Our results have a big contrast to the alternative obtained based on the Schr\"odinger wavefunction representation. Hence, the work points to a very different approach to quantum gravity., Comment: 24 pages in RevTex, no figure

Dirac talked about q-numbers versus c-numbers. Quantum observables are q-number variables that generally do not commute among themselves. He was proposing to have a generalized form of numbers as elements of a noncommutative algebra. That was Dirac's appreciation of the mathematical properties of the physical quantities as presented in Heisenberg's new quantum theory. After all, the familiar real, or complex, number system only came into existence through the history of mathematics. Values of physical quantities having a commutative product is an assumption that is not compatible with quantum physics. The revolutionary idea of Heisenberg and Dirac was pulled back to a much more conservative setting by the work of Schr\"odinger, followed by Born and Bohr. What Bohr missed is that the real number values we obtained from our measurements are only a consequence of the design of the kind of experiments and our using real numbers to calibrate the output scales of our apparatus. It is only our modeling of the information obtained about the physical quantities rather than what Nature dictates. We have proposed an explicit notion of definite noncommutative values of observables that gives a picture of quantum mechanics as realistic as the classical theory. In this article, we illustrate how matrices can be taken as noncommutative (q-)numbers serving as the values of physical quantities, each to be seen as a piece of quantum information. Our main task is to clarify the subtle issues involved in setting up a conventional scheme assigning matrices as values to the physical quantities., Comment: 18 pages in Revtex, no figure

We present an exact quantum observable analog of the weak equivalence principle for a `relativistic' quantum particle. The quantum geodesic equations are obtained from Heisenberg equations of motion as an exact analog of a fully covariant classical Hamiltonian evolution picture, with the proper identification of the canonical momentum variables as $p_\mu$, rather than $p^\mu$. We discuss the meaning of the equations in relation to projective measurements as well as equations with solution curves as ones in the noncommutative geometric picture of spacetime, and a plausible approach to quantum gravity as a theory about quantum observables as physical quantities including the notion of quantum coordinate transformation., Comment: 19 pages in Revtex, no figure; proof-read version published

The famous equation $E=mc^2$ is a version of particle mass being essentially the magnitude of the (energy-)momentum four-vector in the setting of `relativistic' dynamics, which can be seen as dictated by the Poincar\'e symmetry adopted as the relativity symmetry. However, as Einstein himself suggested, the naive notion of momentum as mass times velocity may not be right. The Hamiltonian formulation perspective gives exactly such a setting which in the case of motion of a charged particle under an electromagnetic field actually has the right, canonical, momentum four-vector with an evolving magnitude. The important simple result seems to have missed proper appreciation. In relation to that, we present clear arguments against taking the Poincar\'e symmetry as the fundamental symmetry behind `relativistic' quantum dynamics, and discuss the proper symmetry theoretical formulation and the necessary picture of the covariant Hamiltonian dynamics with an evolution parameter that is, in general, not a particle proper time. In fact, it is obvious that the action of any position operator of a quantum state violates the on-shell mass condition. The phenomenologically quite successful quantum field theories are `second quantized' versions of `relativistic' quantum mechanics. We present a way for some reconciliation of that with our symmetry picture and discuss implications., Comment: 22 pages Revtex, no figure, published version

The locality issue of quantum mechanics is a key issue to a proper understanding of quantum physics and beyond. What has been commonly emphasized as quantum nonlocality has received an inspiring examination through the notion of Heisenberg picture of quantum information. Deutsch and Hayden established a local description of quantum information in a setting of quantum information flow in a system of qubits. With the introduction of a slightly modified version of what we call the Deutsch-Hayden matrix values of observables, together with our recently introduced parallel notion of the noncommutative values from a more fundamental perspective, we clarify all the locality issues based on such values as quantum information carried by local observables in any given arbitrary state of a generic composite system. Quantum information as the {\em `quantum' values} of observables gives a transparent conceptual picture of all the. Spatial locality for a projective measurement is also discussed. The pressing question is if and how such information for an entangled system can be retrieved through local processes which can only be addressed with new experimental thinking., Comment: 28 pages in RevTeX, no figure; proofread version as published except with one equation corrected (marked red)

The Galilei group has been taken as the fundamental symmetry for 'nonrelativistic' physics, quantum or classical. Our fully group theoretical formulation approach to the quantum theory asks for some adjustments. We present a sketch of the full picture here, emphasizing aspects that are different from the more familiar picture. The analysis involves a more careful treatment of the relation between the exact mathematics and its physical application in the dynamical theories, and a more serious full implementation of the mathematical logic than what is usually available in the physics literature. The article summarizes our earlier presented formulation while focusing on the part beyond, with an adjusted, or corrected, identification of the basic representations having the (Newtonian) mass as a Casimir invariant and the notion of center of mass as dictated by the symmetry. Another result is the necessary exclusion of the time translational symmetry, that otherwise bans interactions between particles., Comment: Proof-read version as published

The implications of the physical theory of quantum mechanics on the question of realism is much a subject of sustaining interest, while the background questions among physicists on how to think about all the theoretical notion and `interpretation' of the theory remains controversial. Through a careful analysis of the theoretical notions with the help of modern mathematical perspectives, we give here a picture of quantum mechanics, as the basic theory for `nonrelativistic' particle dynamics, that can be seen as being as much about the physical reality as classical mechanics itself. The key is to fully embrace the noncommutativity of the theory and see it as a notion about the reality of physical quantities. Quantum reality is then just a noncommutative version of the classical reality., Comment: 32 pages of latex, no figure, proofread version to be published

The Galilean symmetry and the Poincare symmetry are usually taken as the fundamental (relativity) symmetries for `nonrelativistic' and `relativistic' physics, respectively, quantum or classical. Our fully group theoretical formulation approach to the theories, together with its natural companion of mechanics from symplectic geometry, ask for different perspectives. We present a sketch of the full picture here, emphasizing aspects which are different from the more familiar picture. The letter summarizes our earlier presented formulation while focusing on the part beyond, with an adjusted, or corrected, identification of the basic representations having the (Newtonian) mass as a Casimir invariant. Discussion on the limitations of the Poincare symmetry for the purpose is particularly elaborated., Comment: Material developed and elaborated in two separate new articles, one focuses only on the `nonrelativistic' case and the other on the `relativistic' case, with different title and authorship

A generic scheme for the parametrization of mixed state systems is introduced, which is then adapted to bipartite systems, especially to a 2-qubit system. Various features of 2-qubit entanglement are analyzed based on the scheme. Our approach exploit much the interplay between is marked by pure states as Hilbert space vectors and mixed states as density matrices, both for the formulation of the parametrization and the analysis of entanglement properties. Explicit entanglement results, in terms of negativity and concurrence, for all 2-qubit mixed states with one single parameter/coordinate among the full set of fifteen being zero and a few other interesting cases are presented., Comment: 18 revtex pages, no figure; proofread version to be publishedd

Based on a recent relational formulation of quantum reference frame transformations, especially with a case of quantum spatial translations in particular, we analyzed how the `value' of an observable for a fixed state change. That is the exact analog of the classical description, for example, of the value of the $x$-coordinate for a particle decrease by 2 units when we perform a translation of the reference frame putting the new origin at $x=2$. The essence of the quantum reference frame transformations is to have the quantum fluctuations, and even entanglement, of the physical object which serves as the (new) reference frame, taken into account. We illustrate how the recently introduced notion of the noncommutative values of quantum observables gives such a definite description successfully. Formulations, and an analysis of a case example in qubit systems, of analog transformations for observables with a discrete or finite spectrum is also presented. Issues about the evolving picture of the symmetry system of all quantum reference frame transformations discussed., Comment: 34 latex pages, no figure

We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski four-vectors under the Lorentz symmetry. The basic representation is identified as a coherent state representation, essentially an irreducible component of the regular representation, with the matching representation of an extension of the group $C^*$-algebra giving the algebra of observables. The key feature of the formulation is that it is not unitary but pseudo-unitary, exactly in the same sense as the Minkowski spacetime representation. The language of pseudo-Hermitian quantum mechanics is adopted for a clear illustration of the aspect, with a metric operator obtained as really the manifestation of the Minkowski metric on the space of the state vectors. Explicit wavefunction description is given without any restriction of the variable domains, yet with a finite integral inner product. The associated covariant harmonic oscillator Fock state basis has all the standard properties in exact analog to those of a harmonic oscillator with Euclidean position and momentum operators of any `dimension'. Galilean limit of the Lorentz symmetry and the classical limit are retrieved rigorously through appropriate symmetry contractions of the algebra and its representation, including the dynamics described through the symmetry of the phase space., Comment: 36 pages. arXiv admin note: substantial text overlap with arXiv:2002.07083

In this pedagogical article, we explore a powerful language for describing the notion of spacetime and particle dynamics intrinsic to a given fundamental physical theory, focusing on special relativity and its Newtonian limit. The starting point of the formulation is the representations of the relativity symmetries. Moreover, that seriously furnishes -- via the notion of symmetry contractions -- a natural way in which one can understand how the Newtonian theory arises as an approximation to Einstein's theory. We begin with the Poincar\'{e} symmetry underlying special relativity and the nature of Minkowski spacetime as a coset representation space of the algebra and the group. Then, we proceed to the parallel for the phase space of a spin zero particle, in relation to which we present the full scheme for its dynamics under the Hamiltonian formulation, illustrating that as essentially the symmetry feature of the phase space geometry. Lastly, the reduction of all that to the Newtonian theory as an approximation with its space-time, phase space, and dynamics under the appropriate relativity symmetry contraction is presented. While all notions involved are well established, the systematic presentation of that story as one coherent picture fills a gap in the literature on the subject matter., Comment: proof-corrected final version: 31 latex pages, no figure

We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski four-vectors under the Lorentz symmetry. The basic representation is identified as a coherent state representation, essentially an irreducible component of the regular representation, with the matching representation of an extension of the group $C^*$-algebra giving the algebra of observables. The key feature of the formulation is that it is not unitary but pseudo-unitary, exactly in the same sense as the Minkowski spacetime representation. Explicit wavefunction description is given without any restriction of the variable domains, yet with a finite integral inner product. The associated covariant harmonic oscillator Fock state basis has all the standard properties in exact analog to those of a harmonic oscillator with Euclidean position and momentum operators of any `dimension'. Galilean limit of the Lorentz symmetry and the classical limit of the Lorentz covariant framework are retrieved rigorously through appropriate symmetry contractions of the algebra and its representation, including the dynamics described through the symmetry of the phase space, given both in terms of real/complex number coordinates and noncommutative operator coordinates. The latter gives an explicit picture of the (projective) Hilbert space as a quantum/noncommutative spacetime., Comment: 35 pages

The earlier treatments of Lorentz covariant harmonic oscillator have brought to light various difficulties, such as reconciling Lorentz symmetry with the full Fock space, and divergence issues with their functional representations. We present here a full solution avoiding those problems. The complete set of Fock states is obtained, together with the corresponding explicit wavefunction and their inner product integrals free from any divergence problem and the Lorentz symmetry fully maintained without additional constraints imposed. By a simple choice of the pseudo-unitary representation of the underlying symmetry group, motivated from the perspective of the Minkowski spacetime as a representation for the Lorentz group, we obtain the natural non-unitary Fock space picture commonly considered though not formulated and presented in the careful details given here. From a direct derivation of the appropriate basis state wavefunctions of the finite-dimensional irreducible representations of the Lorentz symmetry, the relation between the latter and the Fock state wavefunctions is also explicitly shown. Moreover, the full picture including the states with non-positive norm may give consistent physics picture as a version of Lorentz covariant quantum mechanics. Probability interpretation for the usual von Neumann measurements is not a problem as all wavefunctions restricted to a definite value for the `time' variable are just like those of the usual time independent quantum mechanics. A further understanding from a perspective of the dynamics from the symplectic geometry of the phase space is shortly discussed., Comment: 23 pages; corrected coefficients in eq. (12), results unchanged

We illustrate an isomorphic representation of the observable algebra for quantum mechanics in terms of the functions on the projective Hilbert space, and its Hilbert space analog, with a noncommutative product in terms of explicit coordinates and discuss the physical and dynamical picture. The isomorphism is then used as a base for the translation of the differential symplectic geometry of the infinite dimensional manifolds onto the observable algebra as a noncommutative geometry. Hence, we obtain the latter from the physical theory itself. We have essentially an extended formalism of the Schrodinger versus Heisenberg picture which we describe mathematically as like a coordinate map from the phase space, for which we have presented argument to be seen as the quantum model of the physical space, to the noncommutative geometry coordinated by the six position and momentum operators. The observable algebra is taken essentially as an algebra of formal functions on the latter operators. The work formulates the intuitive idea that the noncommutative geometry can be seen as an alternative, noncommutative coordinate, picture of familiar quantum phase space, at least so long as the symplectic geometry is concerned., Comment: 36 pages of revtex, no figure; correct proofread version; the journal published version unfortunately has problems in miss-use of symbols/fonts created by the publisher I am still negotiating for remedies

We discuss the notion about physical quantities as having values represented by real numbers, and its limiting to describe nature to be understood in relation to our appreciation that the quantum theory is a better theory of natural phenomena than its classical analog. Getting from the algebra of physical observables to their values on a fixed state is, at least for classical physics, really a homomorphic map from the algebra into the real number algebra. The limitation of the latter to represent the values of quantum observables with noncommutating algebraic relation is obvious. We introduce and discuss the idea of the noncommutative values of quantum observables and its feasibility, arguing that at least in terms of the representation of such a value as an infinite set of complex number, the idea makes reasonable sense theoretically as well as practically., Comment: 16 pages in latex, no figure; proof-read version

Based on an identified quantum relativity symmetry the contraction of which gives the Newtonian approximation of Galilean relativity, a quantum model of the physical space can be formulated with the Newtonian space seen in a way as the classical approximation. Matching picture for the observable algebra as the corresponding representation of the group C* -algebra, describes the full dynamical pictures equally successfully. Extension of the scheme to a Lorentz covariant setting and beyond will also be addressed.The formulation of quantum mechanics allows the theory to be seen in a new picture in line with the notion of a noncommutative spacetime., Comment: For submission to Proc. of 10th Meeting of Balkan Physics Union, Sofia, Bulgaria

In this article, we utilize the insights gleaned from our recent formulation of space(-time), as well as dynamical picture of quantum mechanics and its classical approximation, from the relativity symmetry perspective in order to push further into the realm of the proposed fundamental relativity symmetry $SO(2,4)$ of our quantum relativity project. We explicitly trace how the diverse actors in this story change through various contraction limits, paying careful attention to the relevant physical units, in order to place all known relativity theories -- quantum and classical -- within a single framework. More specifically, we explore both of the possible contractions of $SO(2,4)$ and its coset spaces in order to determine how best to recover the lower-level theories. These include both new models and all familiar theories, as well as quantum and classical dynamics with and without Einsteinian special relativity. Along the way, we also find connections with covariant quantum mechanics. The emphasis of this article rests on the ability of this language to not only encompass all known physical theories, but to also provide a path for extensions. It will serve as the basic background for more detailed formulations of the dynamical theories at each level, as well as the exact connections amongst them., Comment: 38 pages, 2 tables, published version

The physical world is quantum. However, our description of the quantum physics still relies much on concepts in classical physics and in some cases with `quantized' interpretations. The most important case example is that of spacetime. We examine the picture of the physical space as described by simple, so-called non-relativisitic, quantum mechanics instead of assuming the Newtonian model. The key perspective is that of (relativity) symmetry representation, and the idea that the physical space is to be identified as the configuration space for a free particle. Parallel to the case of the phase space, we have a model of the quantum physical space which reduces to the Newtonian classical model under the classical limit. The latter is to be obtained as a contraction limit of the relativity symmetry., Comment: 9 pages

With approaching quantum/noncommutative models for the deep microscopic spacetime in mind, and inspired by our recent picture of the (projective) Hilbert space as the model of physical space behind basic quantum mechanics, we reformulate here the WWGM formalism starting from the canonical coherent states and taking wavefunctions as expansion coefficients in terms of this basis. This provides us with a transparent and coherent story of simple quantum dynamics where both the wavefunctions for the pure states and operators acting on them arise from the single space/algebra, which exactly includes the WWGM observable algebra. Altogether, putting the emphasis on building our theory out of the underlying relativity symmetry -- the centrally extended Galilean symmetry in the case at hand -- allows one to naturally derive both a kinematical and a dynamical description of a quantum particle, which moreover recovers the corresponding classical picture (understood in terms of the Koopman-von Neumann formalism) in the appropriate (relativity symmetry contraction) limit. Our formulation here is the most natural framework directly connecting all of the relevant mathematical notions and we hope it may help a general physicist better visualize and appreciate the noncommutative-geometric perspective behind quantum physics. It also helps to inspire and illustrate our perspective on looking at quantum mechanics and quantum physics in general in direct connection to the notion of quantum (deformed) relativity symmetries and the corresponding quantum/noncommutative models of spacetime as various levels of approximations all the way down to the Newtonian., Comment: 39 pages, published version

In physics, experiments ultimately inform us as to what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the configuration space of a free particle (or the center of mass of a closed system of particles). This configuration space (as well as phase space), can be constructed as a representation space for the relativity symmetry. From the corresponding quantum symmetry, we illustrate the construction of a quantum configuration space, similar to that of quantum phase space, and recover the classical picture as an approximation through a contraction of the (relativity) symmetry and its representations. The quantum Hilbert space reduces into a sum of one-dimensional representations for the observable algebra, with the only admissible states given by coherent states and position eigenstates for the phase and configuration space pictures, respectively. This analysis, founded firmly on known physics, provides a quantum picture of physical space beyond that of a finite-dimensional manifold, and provides a crucial first link for any theoretical model of quantum spacetime at levels beyond simple quantum mechanics. It also suggests looking at quantum physics from a different perspective., Comment: 19 pages

This is a report on our newly proposed model of dynamical supersymmetry breaking with some details of the analysis involved. The model in the simplest version has only a chiral superfield (multiplet), with a strong four-superfield interaction in the K\"ahler potential that induces a real two-superfield composite with vacuum condensate. The latter has supersymmetry breaking parts, which we show to bear nontrivial solution following basically a standard nonperturbative analysis for a Nambu--Jona-Lasinio type model on a superfield setting. The real composite superfield has a spin one component but is otherwise quite unconventional. We discuss also the parallel analysis for the effective theory with the composite. Plausible vacuum solutions are illustrated and analyzed. The supersymmetry breaking solutions have generated soft mass(es) for the scalar avoiding the vanishing supertrace condition for the squared-masses of the superfield components. We also present some analysis of the resulted low energy effective theory with components of the composite become dynamical. The determinant of the fermionic modes is shown to be zero illustrating the presence of the expected Goldstino. The model gives the possibility of constructing a supersymmetric standard model with all (super)symmetry breaking masses generated dynamically and directly without the necessity of complicated hidden or mediating sectors., Comment: 40 pages, 17 figures

We introduce a simple model of dynamical supersymmetry breaking. It is like a supersymmetric version of a Nambu--Jona-Lasinio model with a spin one composite. The simplest version of the model as presented here has a single chiral superfield (multiplet) with a four-superfield interaction. The latter has the structure of the square of the superfield magnitude square. A vacuum condensate of the latter is illustrated to develop giving rise to supersymmetry breaking with a soft mass term for the superfield. We report also the effective theory picture with a real superfield composite, illustrating the matching effective potential analysis and the vacuum solution conditions for the components. The nature of its fermionic part as the Goldstone mode is presented. Phenomenological application to the supersymmetric standard model is plausible., Comment: 14 pages, 3 figures

This is a review on structure of the fermion mass terms in quantum field theory, under the perspective of its practical applications in the real physics of Nature -- specifically, we discuss fermion mass structure in the Standard Model of high energy physics, which successfully describes fundamental physics up to the TeV scale. The review is meant to be pedagogical, with detailed mathematics presented beyond the level one can find any easily in the textbooks. The discussions, however, bring up important subtleties and ambiguities about the subject that may be less than well appreciated. In fact, the naive perspective of the nature and masses of fermions as one would easily drawn from the presentations of fermion fields and their equations of motion from a typical textbook on quantum field theory leads to some confusing or even wrong statements which we clarify here. In particular, we illustrate clearly that a Dirac fermion mass eigenstate is mathematically equivalent to two degenerated Majorana fermion mass eigenstates at least so long as the mass terms are concerned. There are further ambiguities and subtleties in the exact description of the eigenstate(s). Especially, for the case of neutrinos, the use of the Dirac or Majorana terminology may be mostly a matter of choice. The common usage of such terminology is rather based on the broken $SU(2)$ charges of the related Weyl spinors hence conventional and may not be unambiguously extended to cover more complicate models., Comment: 15 pages. Version published in Annals of Physics

We summarized our report on leptonic flavor violating Higgs decay into mu + tau under the scheme of a generic supersymmetric standard model without R parity. With known experimental constraints imposed, important combinations of R-parity violating parameters which can give notable branching ratios are listed., Comment: Proceeding of SUSY2012 conference. 4 pages

In this paper we examine thoroughly the Higgs boson to mu tau decay via processes involving R parity violating couplings. By means of full one-loop diagrammatic calculations, we found that even if known experimental constraints, particularly including the stringent sub-eV neutrino mass bounds, give strong restrictions on some of the R parity violating parameters, the branching ratio could still achieve notable value in the admissible parameter space. Hence, the flavor violating leptonic decay is of interest to future experiments. We present here key results of our analysis. Based on the analysis, we give some comments on h -> e mu and h -> e tau also., Comment: 35 pages, 3 figures, 8 tables. Version published in Physical Review D

In this letter, we report on lepton flavor violating Higgs decay into mu+tau in the framework of the generic supersymmetric standard model without R parity and list interesting combinations of R-parity violating parameters. We impose other known experimental constraints on the parameters of the model and show our results from the R-parity violating parameters. In our analysis, the branching ratio of Higgs to mu+tau can exceed 10^{-5} within admissible parameter space., Comment: 16 pages, 3 figures, 1 table. Version published in Europhysics Letters

We study the theoretical features in relation to dynamical mass generation and symmetry breaking for the recently proposed holomorphic supersymmetric Nambu--Jona-Lasinio model. The basic model has two different chiral superfields (multiplets) with a strongly coupled dimension five four-superfield interaction. In addition to the possibility of generation of Dirac mass between the pair established earlier, we show here the new option of generation of Majorana masses for each chiral superfield. We also give a first look at what condition may prefer Dirac over Majorana mass, illustrating that a split in the soft supersymmetry breaking masses is crucial. In particular, in the limit where one of the soft masses vanish, we show that generation of the Majorana mass is no longer an option, while the Dirac mass generation survives well. The latter is sensitive mostly to the average of the two soft masses. The result has positive implication on the application of the model framework towards dynamical electroweak symmetry breaking with Higgs superfields as composites., Comment: 15 pages, 1 figure. Revised version matches the accepted one for publication in Phy.Rev.D Journal

With a more relaxed perspective on what constitutes a relativity symmetry mathematically, we revisit the notion of possible relativity or kinematic symmetries mutually connected through Lie algebra contractions. We focus on the contractions of an $SO(m,n)$ symmetry as a relativity symmetry on an $m+n$ dimension geometric arena, which generalizes the notion of spacetime, and discuss systematically contractions that reduce the dimension one at a one, aiming at going one step beyond what has been discussed in the literature. Our key results are five different contractions of a Galilean-type symmetry G(m,n) preserving a symmetry of the same type at dimension $m+n-1$, e.g. a G(m,n-1), together with the coset space representations that correspond to the usual physical picture. Most of the results are explicitly illustrated through the example of symmetries obtained from the contraction of SO(2,4), which is the particular case for our interest on the physics side as the proposed relativity symmetry for "quantum spacetime". The contractions from G(1,3) may be relevant to real physics., Comment: 23 pages in revtex with 1 figure incorporated

In this paper we discuss Nambu-Jona-Lasinio model as a classical model for dynamical mass generation and symmetry breaking. In addition we discuss the possible supersymmetric extensions of this model resulting from interaction terms with four chiral superfields that may be regarded as a supersymmetric generalization of the four-fermion interactions of the Nambu-Jona-Lasinio model. A four-superfield interaction terms can be constructed as either dimension 6 or dimension 5 operators. Through analyzing solutions to the gap equations, we discuss the dynamical generation of superfield Dirac mass, including a supersymmetry breaking part. A dynamical symmetry breaking generally goes along with the dynamical mass generation, for which a bi-superfield condensate is responsible., Comment: 7 pages, 2 figures, talk presented in the 2011 International Workshop on Future Linear Colliders (LCWS11), Granada, Spain

We investigate the dynamical mass generation resulted from interaction terms with four chiral superfields. The kind of interactions maybe considered a supersymmetric generalization of the four-fermion interactions of the classic Nambu--Jona-Lasinio model. A four-superfield interaction that contains a four-fermion interaction as one of its component terms has been the standard supersymmetrization of the NJL model for decades. Recently, we introduced a holomorphic variant with a dimension five interaction term instead. The latter is a main target of the present analysis. With the introduction of a new perspective on the superfield gap equation, we derive it for each one of the four-superfield interactions, using the supergraph technique. Through analyzing solutions to the gap equations, we illustrate the dynamical generation of superfield Dirac mass, including a supersymmetry breaking part. A dynamical symmetry breaking generally goes along with the dynamical mass generation, for which a bi-superfield condensate is responsible. The explicit illustration of dynamical symmetry breaking from the holomorphic dimension five interaction is reported for the first time. It has rich and novel features, which would be easily missed without the superfield approach developed here. We also discuss the nature of the bi-superfield condensate and its role of the effective Higgs superfield picture for both cases, illustrating their difference. Note that such a holomorphic quark superfield interaction term can successful account for the electroweak symmetry breaking with Higgs superfields as composites.

The Poincar\'e-Snyder relativity was introduced in an earlier paper of ours as an extended form of Einstein relativity obtained by appropriate limiting setting of the full Quantum Relativity. The latter, with fundamental constants $\hbar$ and $G$ built into the symmetry, is supposed to be the relativity of quantum space-time. Studying the mechanics of Poincar\'e-Snyder relativity is an important means to get to confront the great challenge of constructing the dynamics of Quantum Relativity. The mechanics will also be of interest on its own, plausibly yielding prediction accessible to experiments. We write the straightforward canonical formulation here, and show that it yields sensible physics pictures. Besides the free particle case, we also give an explicit analysis of two particle collision as dictated by the formulation, as well as the case of a particle rebouncing from an insurmountable potential barrier in the time direction. The very interesting solution of particle-antiparticle creation and annihilation as interpreted in a the usual time evolution picture can be obtained, in the simple classical mechanics setting. We consider that a nontrivial success of the theory, giving confidence that the whole background approach is sensible and plausibly on the right track. We also sketch the quantum mechanics formulation, direct from the familiar canoincal quantization, matching to a relativity group geometric quantization formulation in a previous publication., Comment: 27 pages in Revtex; 2 figures in 3 eps files incorporated

Based on a linear realization formulation of a quantum relativity -- the proposed relativity for quantum `space-time', we introduce the Poincar\'e-Snyder relativity and Snyder relativity as relativities in between the latter and the well known Galilean and Einstein cases. We discuss how the Poincar\'e-Snyder relativity may provide a stronger framework for the description of the usual (Einstein) relativistic quantum mechanics and beyond. In particular, we discuss a geometric quantization picture through the U(1) central extension of the relativity group, which had been establish to work well for the Galilean case but not for the Einstein case. We discuss similarities and differences between our Poincar\'e-Snyder picture with a still not fully understood $\sigma$ variable as the `evolution' parameter and some use of an invariant time or the proper time parameter in some earlier formulations with very similar mathematical structure. The study is a first step towards the investigation of physics of the $\sigma$ variable at the Poincar\'e-Snyder setting, plausible leading to experimental signatures to be studied., Comment: 17 pages in revtex, no figure

We discuss a 4D noncommutative space-time as suggested by the version of quantum (deformed) relativity which provides a classical geometry picture as an `AdS_5'. The 4D noncommutative space-time is more like a part of a phase space description, in accordance with the quantum notion -- quantum mechanics talks about only states but not configurations. The `AdS_5' picture also illustrates the classical 4D space-time is to be described as part of a bigger geometry beyond space-time at the quantum level. The radically new picture of quantum 'space-time' is expected to provide the basis for a (still to be formulated) new approach to quantum gravity with fundamental constants (quantum) hbar and Newton's constant G put at a similar level as c, the speed of light., Comment: 8 pages latex, talk given at SMP 40 (2008), Torun, Poland

We study the electric dipole moment (EDM) and the anomalous magnetic dipole moment (MDM) of the muon in the CP-violating Minimal Supersymmetric extension of the Standard Model (MSSM). We take into account the contributions from the chargino- and neutralino-mediated one-loop graphs and the dominant two-loop Higgs-mediated Barr-Zee diagrams. We improve earlier calculations by incorporating CP-violating Higgs-boson mixing effects and the resummed threshold corrections to the Yukawa couplings of the charged leptons as well as that of the bottom quark. The analytic correlation between the muon EDM and MDM is explicitly presented at one- and two-loop levels and, through several numerical examples, we illustrate its dependence on the source of the dominant contributions. We have implemented the analytic expressions for the muon EDM and MDM in an updated version of the public code CPsuperH2.0., Comment: 26 pages, 10 figures, references added, more references added, to appear in JHEP

We present a detailed analysis together with exact numerical calculations on one-loop contributions to the branching ratio of the radiative decay of $\mu$ and $\tau$, namely $\mu \to e \gamma$, $\tau \to e \gamma$, and $\tau \to\mu \gamma$ from supersymmetry without R parity, focusing on contributions involving bilinear couplings. A numerical study is performed to obtain explicit bounds on the parameters under the present experimental limit. We present, and use in the calculation, formulas for exact mass eigenstate effective couplings. In this sense, we present an exact analysis free from approximation for the first time. After comparing our results against the closest early analysis, we discovered a major difference in resulted constraints on some ${\mu_i^*} {B_j}$ combinations. Constraints from neutrino masses on the parameters were considered. Our result indicates that the branching ratio measurement on $\mu \to e \gamma$ down to $10^{-13}-10^{-14}$ and beyond, as targeted by the MEG experiment, has a chance of observing decay from the R-parity violating scenario., Comment: Comments: 24 pages, 12 figures, 3 table, RevTex; Corrected typos, 2 added references for section 1. The proof-read version to be published in Phys. Rev. D

We present a detailed analysis of the neutron, deuteron and mercury electric dipole moment from supersymmetry without R parity, focusing on the quark-scalar loop contributions. Being proportional to top Yukawa and top mass, such contributions are often large. Analytical expressions illustrating the explicit role of the R-parity violating parameters are given following perturbative diagonalization of mass-squared matrices for the scalars. Dominant contributions come from the combinations $B_i \lambda^{\prime}_{ij1}$ for which we obtain robust bounds. It turns out that neutron and deuteron EDMs receive much stronger contributions than mercury EDM and any null result at the future deuteron EDM experiment or Los Alamos neutron EDM experiment can lead to extra-ordinary constraints on RPV parameter space. Even if R-parity violating couplings are real, CKM phase does induce RPV contribution and for some cases such a contribution is as strong as contribution from phases in the R-parity violating couplings.Hence, we have bounds directly on $|B_i \lambda^{\prime}_{ij1}|$ even if the RPV parameters are all real. Interestingly, even if slepton mass and/or $\mu_0$ is as high as 1 TeV, it still leads to neutron EDM that is an order of magnitude larger than the sensitivity at Los Alamos experiment. Since the results are not much sensitive to $\tan \beta$, our constraints will survive even if other observables tighten the constraints on $\tan \beta$., Comment: 16 pages, 10 figures, accepted for publication in Physical Review D

Quantum relativity as a generalized, or rather deformed, version of Einstein relativity with a linear realization on a classical six-geometry beyond the familiar setting of space-time offer a new framework to think about the quantum space-time structure. The formulation requires two deformations to be implemented through imposing two fundamental invariants. We take them to be the independent Planck mass and Planck length. Together, they gives the quantum $\hbar$. The scheme leads to {\small \boldmath\protect SO(2,4)} as the relativity symmetry. The quantum world has an AdS$_5$ `classical' geometry, which is parallel to the "conformal universe", but not scale invariant., Comment: 10 pages of revtex, no figure;a largely rewritten presentation of the same results

We study the flavor changing neutral current decays of the MSSM Higgs bosons into strange and bottom quarks. We focus on a scenario of minimum flavor violation here, namely only that induced by the CKM matrix. Taking into account constraint from $b\to s \gamma$, $\delta\rho$ as well as experimental constraints on the MSSM spectrum, we show that the branching ratio of $(\Phi\to b\bar{s})$ and $(\Phi \to \bar{b}s)$ combined, for $\Phi$ being either one of the CP even Higgs states, can reach the order $10^{-4}$-$10^{-3}$ for large $\tan\beta$, large $\mu$, and large $A_t$. The result illustrates the significance of minimal flavor violation scenario which can induce competitive branching fraction for flavor changing Higgs decays. This can be compared with the previous studies where similar branching fraction has been reported, but with additional sources of flavor violations in squark mass matrices. We also discuss some basic features of the flavor violating decays in the generic case., Comment: 16 pages on Revtex, with 5 figures from 10 eps files incorporated; discussion on issues related more precise calculations elaborated; proof-edited version to appear in Phys. Lett. B

The idea of quantum relativity as a generalized, or rather deformed, version of Einstein (special) relativity has been taking shape in recent years. Following the perspective of deformations, while staying within the framework of Lie algebra, we implement explicitly a simple linear realization of the relativity symmetry, and explore systematically the resulting physical interpretations. Some suggestions we make may sound radical, but are arguably natural within the context of our formulation. Our work may provide a new perspective on the subject matter, complementary to the previous approach(es), and may lead to a better understanding of the physics., Comment: 27 pages in Revtex, no figure; proof-edited version to appear in Phys.Rev.D

We present a detailed analysis together with numerical calculations on one-loop contributions to the neutron electric dipole moment from supersymmetry without R parity, focusing on the quark-scalar loop contributions. Complete formulas are given for the various contributions through the quark dipole operators. Analytical expressions illustrating the explicit role of the R-parity violating parameters are given following perturbative diagonalization of mass-squared matrices for the scalars. Dominant contributions come from the combinations $B_i^{\ast} \lambda^{\prime}_{ij1}$ for which we obtain robust bounds. Even if the R-parity violating couplings are real, CKM phase does induce RPV contribution and for some cases such a contribution is as strong as contribution from phases in the R-parity violating couplings. Hence, we have bounds directly on $|B_i^{\ast} \l^{\prime}_{ij1}|$ even if the parameters are all real., Comment: 16 pages, 5 figures

We present a systematic analysis of the decay B--> X_s + gamma at the leading log within the framework of Supersymmetry without R-parity. We point out some new contributions in the form of bilinear-trilinear combination of R-parity violating (RPV) couplings that are enhanced by large tanbeta. We also improve by a few orders of magnitude, bounds on several combinations of R-parity violating parameters., Comment: 5 pages latex. Based on talk given by R. Vaidya at the Pran Nath Fest and PASCOS'04 North-Eastern University, Boston. Necessary style files included

We present a systematic analysis of the decay b --> s gamma at the leading log within the framework of Supersymmetry without R-parity. We point out some new contributions in the form of bilinear-trilinear combination of R-parity violating (RPV) couplings that are enhanced by large tanbeta. We also improve by a few orders of magnitude, bounds on several combinations of RPV parameters., Comment: 4 pages. Talk given by R. Vaidya at the SUSY-2004 conference, Tsukuba, Japan, June 17-23, 2004. Title slightly changed from the conference talk. Style file pdproc.sty included

The implementation of the little Higgs mechanism to solve the hierarchy problem provides an interesting guiding principle to build particle physics models beyond the electroweak scale. Most model building works, however, pay not much attention to the fermionic sector. Through a case example, we illustrate how a complete and consistent fermionic sector of the TeV effective field theory may actually be largely dictated by the gauge structure of the model. The completed fermionic sector has specific flavor physics structure, and many phenomenological constraints on the model can thus be obtained beyond gauge, Higgs, and top physics. We take a first look on some of the quark sector constraints., Comment: 14 revtex pages with no figure, largely a re-written version of hep-ph/0307250 with elaboration on flavor sector FCNC constraints; accepted for publication in Phys.Rev.D

The little Higgs mechanism provides an alternative solution to the hierarchy problem, arguably fitting better into the phenomenological hint of the "little hierarchy" which may cause some fine-tuning for the case of supersymmetry. We discuss an aspect of little Higgs physics lacking proper attention -- the construction of an interesting and consistent chiral fermionic sector and its phenomenological implications. At least for the kind of example models to be discussed, the gauge and top sector structure of a model largely dictates, through gauge anomaly cancellation conditions, a specific chiral fermion spectrum. The spectrum has interesting, family non-universal, flavor structure. The implications for flavor physics are specially interesting. We also add a brief comment of little Higgs versus supersymmetry., Comment: $+1 latex pages with pdproc.sty (attached); talk given at SUSY '04

We present a systematic analysis at the leading log order of the influence of combination of bilinear and trilinear R-parity violating couplings on the decay b-->s gamma. Such contributions have never been explored in the context of this decay. We show that influence of charged-slepton-Higgs mixing mediated loops can dominate the SM and MSSM contributions and hence can provide strong bounds on the combination of bilinear-trilinear R-parity violating couplings. Such contributions are also enhanced by large tan beta. With substantially extended basis of operators (28 operators), we provide illustrative analytical formulae of the major contributions to complement our complete numerical results which demonstrate the importance of QCD running effects., Comment: 4 pages, 2 figures

We discuss extensions of the Standard Model through extending the electroweak gauge symmetry. An extended electroweak symmetry requires a list of extra fermionic and scalar states. The former is necessary to maintain cancellation of gauge anomalies, and largely fixed by the symmetry embedding itself. The latter is usually considered quite arbitrary, so long as a vacuum structure admitting the symmetry breaking is allowed. Anomaly cancellation may be used to link the three families of quarks and leptons together, given a perspective on flavor physics. It is illustrated lately that the kind of models may also have the so-called little Higgs mechanism incorporated. This more or less fixes the scalar sector and take care of the hierarchy problem, making such models of extended electroweak symmetries quite appealing candidates as TeV scale effective field theories., Comment: 1+8 pages of latex with ws-procs9x6.cls; talk presented at Coral Gables Conference 2003

We present a systematic analysis of all the contributions at the leading log order to the branching ratio of the inclusive radiative B decay, B --> X_s + gamma in the framework of supersymmetry without R-parity. The relevant set of four-quark operators involved in QCD running are extended from 6 (within SM and MSSM) to 24, with also many new contributions to the Wilson coefficients of (chromo)magnetic penguins for either chiral structure. We present complete analytical results here without any a priori assumptions on the form of R-parity violation. Mass eigenstate expressions are given, hence the results are free from the commonly adopted mass-insertion approximation. In the numerical analysis, we focus here only on the influence of the trilinear lambda-prime couplings and report on the possibility of a few orders of magnitude improvement for the bounds on a few combinations of the lambda-prime couplings. Our study shows that the Wilson coefficients of the current-current operators due to R-parity violation dominate over the direct contributions to the penguins. However, the inter-play of various contributions is complicated due to the QCD corrections which we elaborate here., Comment: 26 pages, 13 figures. A few typos corrected and a few references added. Contents and results unchanged

Interesting contributions to $\Delta a_\mu$ from a two-Higgs-doublet-model is coming from a two-loop Barr-Zee diagram for most part of the parameter space -- a fact that has been overlooked by some Higgs/SUSY experts. A definite positive contribution has requirements that go against precision EW data and other known constraints. For the case without SUSY, in particular, this is almost enough to kill the two-Higgs-doublet-model (II). We will discuss the interplay of all the constraints and their implications., Comment: 1+4 pages of latex with ws-procs9x6.cls,5 figure postscripts included; talk at SUSY03

We discuss the proper starting point to look into flavor physics under the perspective of solving the hierarchy problem with the little Higgs mechanism -- the construction of anomaly free fermionic spectra of the effective theory of extended electroweak gauge symmetry around the TeV scale. Anomaly cancellations among the three SM families, plus extra fermions, are typically needed, giving family non-universal flavor structures. Such a completed and consistent fermionic spectrum supplements a scalar sector little Higgs model, turning the latter into a realistic model the phenomenological viability of which can then be investigated. The implications for flavor physics are specially interesting. We give more elaborated discussion here on our basic perspective, trying to clarify on issues that are in our opinion under-appreciated. We also add a brief comment of little Higgs versus supersymmetry., Comment: 6 pages in revtex; Invited Talk at the 2nd International Conference on Flavor Physics (Oct 2003)