Search

Abstract We explain how stochastic TQFT supersymmetry can be made compatible with space supersymmetry. Taking the case of N = 2 supersymmetric quantum mechanics, (the proof would be the same for the Wess–Zumino model), we determine the kernels that ensure the convergence of the stochastic process toward the standard path integral, under the condition that they are covariant under supersymmetry. They depend on a massive parameter M that can be chosen at will and modifies the course of the stochastic evolution, but the infinite stochastic time limit of the correlation functions is in fact independent on the choice of M. [ABSTRACT FROM AUTHOR]

Abstract The gluon propagator plays a central role in determining the dynamics of QCD. In this work we demonstrate for BRST quantised QCD that the Dyson–Schwinger equation imposes significant analytic constraints on the structure of this propagator. In particular, we find that these constraints control the appearance of massless components in the gluon spectral density. [ABSTRACT FROM AUTHOR]

Abstract We show a possibility for the charge quantization of the standard model (SM) particles. If a global symmetry makes the three copies of a generation and supersymmetry (SUSY) relates the Higgs boson to a lepton, all the charges of the SM particles can be quantized through gauge-anomaly cancellation. In the minimal model realizing the possibility, the gravitino mass around the Planck-scale is needed to generate the SM couplings through (quantum) supergravity. Much below the Planck-scale, the SM with non-vanishing neutrino masses is obtained as the effective theory. As extensions of the SM with this quantization mechanism, millicharged particles can exist without introducing massless hidden photons. [ABSTRACT FROM AUTHOR]

Abstract The concept of effective dynamics has proven successful in LQC, a loop-inspired quantization of cosmological spacetimes. We apply the same idea of its derivation in LQC to the full theory, by computing the expectation value of the scalar constraint with respect to some coherent states peaked on the phase-space variables of flat Robertson–Walker spacetime. We comment on the relation with effective LQC and find a deviation stemming from the Lorentzian part of the Hamiltonian. [ABSTRACT FROM AUTHOR]

We evaluate the frame-independent gluon and charm parton-distribution functions (PDFs) of the deuteron utilizing light-front quantization and the impulse approximation. We use a nuclear wave function obtained from solving the nonrelativistic Schrödinger equation with the realistic Argonne v18 nuclear force, which we fold with the proton PDF. The predicted gluon distribution in the deuteron (per nucleon) is a few percent smaller than that of the proton in the domain x b j = Q 2 2 p N ⋅ q ∼ 0.4 , whereas it is strongly enhanced for x b j larger than 0.6. We discuss the applicability of our analysis and comment on how to extend it to the kinematic limit x b j → 2 . We also analyze the charm distribution of the deuteron within the same approach by considering both the perturbatively and non-perturbatively generated (intrinsic) charm contributions. In particular, we note that the intrinsic-charm content in the deuteron will be enhanced due to 6-quark “hidden-color” QCD configurations. [ABSTRACT FROM AUTHOR]

We present simple solutions of IKKT-type matrix models describing a quantized homogeneous and isotropic cosmology with k = − 1 , finite density of microstates and a resolved Big Bang. At late times, a linear coasting cosmology a ( t ) ∝ t is obtained, which is remarkably close to observation. The solution consists of two sheets with opposite intrinsic chiralities, which are connected in a Euclidean pre-big bang era. [ABSTRACT FROM AUTHOR]

A way to encode acceleration directly into fields has recently being proposed, thus establishing a new kind of fields, the accelerated fields. The definition of accelerated fields points to the quantization of space and time, analogously to the way quantities like energy and momentum are quantized in usual quantum field theories. Unruh effect has been studied in connection with quantum field theory in curved spacetime and it is described by recruiting a uniformly accelerated observer. In this work, as a first attempt to demonstrate the utility of accelerated fields, we present an alternative way to derive Unruh effect. We show, by studying quantum field theory on quantum spacetime, that Unruh effect can be obtained without changing the reference frame. Thus, in the framework of accelerated fields, the observational confirmation of Unruh effect could be assigned to the existence of quantum properties of spacetime. [ABSTRACT FROM AUTHOR]

We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental “phase-spacetime”. We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantum mechanics purely geometric, and possibly even topological. Our approach is especially useful for time-dependent problems and systems subject to ambiguities in choices of clock or observer. As a byproduct, we give a derivation and generalization of the Wigner functions of standard quantum mechanics. [ABSTRACT FROM AUTHOR]

Development of quantum gravity theories rarely takes inputs from experimental physics. In this letter, we take a small step towards correcting this by establishing a paradigm for incorporating putative quantum corrections, arising from canonical quantum gravity (QG) theories, in deriving falsifiable modified dispersion relations (MDRs) for particles on a deformed Minkowski space–time. This allows us to differentiate and, hopefully, pick between several quantization choices via testable, state-of-the-art phenomenological predictions. Although a few explicit examples from loop quantum gravity (LQG) (such as the regularization scheme used or the representation of the gauge group) are shown here to establish the claim, our framework is more general and is capable of addressing other quantization ambiguities within LQG and also those arising from other similar QG approaches. [ABSTRACT FROM AUTHOR]

Quantization of the bosonic string around the classical, perturbative vacuum is not consistent for spacetime dimensions 2 < d < 26 . Recently we have showed that at large d there is another so-called mean-field vacuum. Here we extend this mean-field calculation to finite d and show that the corresponding mean-field vacuum is stable under quadratic fluctuations for 2 < d < 26 . We point out the analogy with the two-dimensional O ( N ) -symmetric sigma-model, where the 1 / N -vacuum is very close to the real vacuum state even for finite N , in contrast to the perturbative vacuum. [ABSTRACT FROM AUTHOR]

Using the charmonium light-front wavefunctions obtained by diagonalizing an effective Hamiltonian with the one-gluon exchange interaction and a confining potential inspired by light-front holography in the basis light-front quantization formalism, we compute production of charmonium states in diffractive deep inelastic scattering and ultra-peripheral heavy ion collisions within the dipole picture. Our method allows us to predict yields of all vector charmonium states below the open flavor thresholds in high-energy deep inelastic scattering, proton–nucleus and ultra-peripheral heavy ion collisions, without introducing any new parameters in the light-front wavefunctions. The obtained charmonium cross section is in reasonable agreement with experimental data at HERA, RHIC and LHC. We observe that the cross-section ratio σ Ψ ( 2 s ) / σ J / Ψ reveals significant independence of model parameters. [ABSTRACT FROM AUTHOR]

Full general relativity is almost certainly ‘chaotic’. We argue that this entails a notion of non-integrability: a generic general relativistic model, at least when coupled to cosmologically interesting matter, likely possesses neither differentiable Dirac observables nor a reduced phase space. It follows that the standard notion of observable has to be extended to include non-differentiable or even discontinuous generalized observables. These cannot carry Poisson-algebraic structures and do not admit a standard quantization; one thus faces a quantum representation problem of gravitational observables . This has deep consequences for a quantum theory of gravity, which we investigate in a simple model for a system with Hamiltonian constraint that fails to be completely integrable. We show that basing the quantization on standard topology precludes a semiclassical limit and can even prohibit any solutions to the quantum constraints. Our proposed solution to this problem is to refine topology such that a complete set of Dirac observables becomes continuous. In the toy model, it turns out that a refinement to a polymer-type topology, as e.g. used in loop gravity, is sufficient. Basing quantization of the toy model on this finer topology, we find a complete set of quantum Dirac observables and a suitable semiclassical limit. This strategy is applicable to realistic candidate theories of quantum gravity and thereby suggests a solution to a long-standing problem which implies ramifications for the very concept of quantization. Our work reveals a qualitatively novel facet of chaos in physics and opens up a new avenue of research on chaos in gravity which hints at deep insights into the structure of quantum gravity. [ABSTRACT FROM AUTHOR]

A gauge fixing condition is presented here for non-Abelian gauge theory on the manifold R ⊗ S 1 ⊗ S 1 ⊗ S 1 . It is proved that the new gauge fixing condition is continuous and free from the Gribov ambiguity. While perturbative calculations based on the new gauge condition behave like those based on the axial gauge in ultraviolet region, infrared behaviours of the perturbative series under the new gauge fixing condition are quite nontrivial. The new gauge condition, which reads n ⋅ ∂ n ⋅ A = 0 , may not satisfy the boundary condition A μ ( ∞ ) = 0 as required by conventional perturbative calculations for gauge theories on the manifold S 4 . However, such contradiction is not harmful for the theory considered here. [ABSTRACT FROM AUTHOR]

The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x . Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos–Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics. [ABSTRACT FROM AUTHOR]

How likely is it that there are particles in a vector-like pair of representations in low-energy spectrum, when neither symmetry nor anomaly consideration motivates their presence? We address this question in the context of supersymmetric and geometric phase compactification of F-theory and Heterotic dual. Quantisation of the number of generations (or net chiralities in more general term) is also discussed along the way. Self-dual nature of the fourth cohomology of Calabi–Yau fourfolds is essential for the latter issue, while we employ Brill–Noether theory to set upper bounds on the number ℓ of vector-like pairs of chiral multiplets in the SU ( 5 ) GUT ( 5 + 5 ¯ ) representations. For typical topological choices of geometry for F-theory compactification for SU(5) unification, the range of 0 ≤ ℓ ≲ 4 for perturbative unification is not in immediate conflict with what is already understood about F-theory compactification at this moment. [ABSTRACT FROM AUTHOR]

We study the heavy quarkonium within the basis light-front quantization approach. We implement the one-gluon exchange interaction and a confining potential inspired by light-front holography. We adopt the holographic light-front wavefunction (LFWF) as our basis function and solve the non-perturbative dynamics by diagonalizing the Hamiltonian matrix. We obtain the mass spectrum for charmonium and bottomonium. With the obtained LFWFs, we also compute the decay constants and the charge form factors for selected eigenstates. The results are compared with the experimental measurements and with other established methods. [ABSTRACT FROM AUTHOR]

The quantum genesis of Hawking radiation is a long-standing puzzle in black hole physics. Semi-classically one can argue that the spectrum of radiation emitted by a black hole look very much sparse unlike what is expected from a thermal object. It was demonstrated through a simple quantum model that a quantum black hole will retain a discrete profile, at least in the weak energy regime. However, it was suggested that this discreteness might be an artifact of the simplicity of eigen-spectrum of the model considered. Different quantum theories can, in principle, give rise to different complicated spectra and make the radiation from black hole dense enough in transition lines, to make them look continuous in profile. We show that such a hope from a geometry-quantized black hole is not realized as long as large enough black holes are dubbed with a classical mass area relation in any gravity theory ranging from GR, Lanczos–Lovelock to f(R) gravity. We show that the smallest frequency of emission from black hole in any quantum description, is bounded from below, to be of the order of its inverse mass. That leaves the emission with only two possibilities. It can either be non-thermal, or it can be thermal only with the temperature being much larger than 1/M. [ABSTRACT FROM AUTHOR]

We investigate the non-Abelian Aharonov–Bohm (AB) effect for time-dependent gauge fields. We prove that the non-Abelian AB phase shift related to time-dependent gauge fields, in which the electric and magnetic fields are written in the adjoint representation of SU ( N ) generators, vanishes up to the first order expansion of the phase factor. Therefore, the flux quantization in a superconductor ring does not appear in the time-dependent Abelian or non-Abelian AB effect. [ABSTRACT FROM AUTHOR]

We suggest and briefly review a new sort of superrenormalizable models of higher derivative quantum gravity. The higher derivative terms in the action can be introduced in such a way that all the unphysical massive states have complex poles. According to the literature on Lee–Wick quantization, in this case the theory can be formulated as unitary, since all massive ghosts-like degrees of freedom are unstable. [ABSTRACT FROM AUTHOR]

Prominent approaches to quantum gravity struggle when it comes to incorporating a positive cosmological constant in their models. Using quantization of a complex SL ( 2 , C ) Chern–Simons theory we include a cosmological constant, of either sign, into a model of quantum gravity. [ABSTRACT FROM AUTHOR]

The inflationary paradigm is an important cornerstone of the concordance cosmological model. However, standard inflation cannot fully address the transition from an early homogeneous and isotropic stage, to another one lacking such symmetries corresponding to our present universe. In previous works, a self-induced collapse of the wave function has been suggested as the missing ingredient of inflation. Most of the analysis regarding the collapse hypothesis has been solely focused on the characteristics of the spectrum associated to scalar perturbations, and within a semiclassical gravity framework. In this Letter, working in terms of a joint metric-matter quantization for inflation, we calculate, for the first time, the tensor power spectrum and the tensor-to-scalar ratio corresponding to the amplitude of primordial gravitational waves resulting from considering a generic self-induced collapse. [ABSTRACT FROM AUTHOR]

We consider field quantization on an arbitrary null hypersurface in curved spacetime. We discuss the de Sitter horizon as the simplest example, relating the horizon quantization to the standard Fock space in the cosmological patch. We stress the universality of null-hypersurface kinematics, using it to generalize the Unruh effect to vacuum or thermal states with respect to null “time translations” on arbitrary (e.g. non-stationary) horizons. Finally, we consider a general pure state on a null hypersurface, which is divided into past and future halves, as when a bifurcation surface divides an event horizon. We present a closed-form recipe for reducing such a pure state into a mixed state on each half-hypersurface. This provides a framework for describing entanglement between spacetime regions directly in terms of their causal horizons. To illustrate our state-reduction recipe, we use it to derive the Unruh effect. [ABSTRACT FROM AUTHOR]

We show that the spherically symmetric isolated horizon can be described in terms of an SU ( 2 ) connection and an su ( 2 ) -valued one-form, obeying certain constraints. The horizon symplectic structure is precisely the one of 3d gravity in a first order formulation. We quantize the horizon degrees of freedom in the framework of loop quantum gravity, with methods recently developed for 3d gravity with non-vanishing cosmological constant. Bulk excitations ending on the horizon act very similarly to particles in 3d gravity. The Bekenstein–Hawking law is recovered in the limit of imaginary Barbero–Immirzi parameter. Alternative methods of quantization are also discussed. [ABSTRACT FROM AUTHOR]

The recently proposed UV self-complete quantum gravity program is a new and very interesting way to envision Planckian/trans-Planckian physics. In this new framework, high energy scattering is dominated by the creation of micro black holes, and it is experimentally impossible to probe distances shorter than the horizon radius. In this letter we present a model which realizes this idea through the creation of self-regular quantum black holes admitting a minimal size extremal configuration. Their radius provides a dynamically generated minimal length acting as a universal short-distance cutoff. We propose a quantization scheme for this new kind of microscopic objects based on a Bohr-like approach, which does not require a detailed knowledge of quantum gravity. The resulting black hole quantum picture resembles the energy spectrum of a quantum harmonic oscillator. The mass of the extremal configuration plays the role of zero-point energy. Large quantum number re-establishes the classical black hole description. Finally, we also formulate a “quantum hoop conjecture” which is satisfied by all the mass eigenstates and sustains the existence of quantum black holes sourced by Gaussian matter distributions. [ABSTRACT FROM AUTHOR]

We present a common solution to the puzzles of the light Higgs or quark masses and the need for a shift symmetry and large field values in high scale chaotic inflation. One way to protect, for example, the Higgs from a large supersymmetric mass term is if it is the Nambu–Goldstone boson (NGB) of a nonlinear sigma model. However, it is well known that nonlinear sigma models (NLSMs) with nontrivial Kähler transformations are problematic to couple to supergravity. An additional field is necessary to make the Kähler potential of the NLSM invariant in supergravity. This field must have a shift symmetry — making it a candidate for the inflaton (or axion). We give an explicit example of such a model for the coset space SU ( 3 ) / SU ( 2 ) × U ( 1 ) , with the Higgs as the NGB, including breaking the inflaton's shift symmetry and producing a chaotic inflation potential. This construction can also be applied to other models, such as one based on E 7 / SO ( 10 ) × U ( 1 ) × U ( 1 ) which incorporates the first two generations of (light) quarks as the Nambu–Goldstone multiplets, and has an axion in addition to the inflaton. Along the way we clarify and connect previous work on understanding NLSMs in supergravity and the origin of the extra field (which is the inflaton here), including a connection to Witten–Bagger quantization. This framework has wide applications to model building; a light particle from a NLSM requires, in supergravity, exactly the structure for chaotic inflaton or an axion. [ABSTRACT FROM AUTHOR]

We explain how an unexpected algebraic structure, the division algebras, can be seen to underlie a generation of quarks and leptons. From this new vantage point, electrons and quarks are simply excitations from the neutrino, which formally plays the role of a vacuum state. Using the ladder operators which exist within the system, we build a number operator in the usual way. It turns out that this number operator, divided by 3, mirrors the behaviour of electric charge. As a result, we see that electric charge is quantized because number operators can only take on integer values. Finally, we show that a simple hermitian form, built from these ladder operators, results uniquely in the nine generators of SU c ( 3 ) and U em ( 1 ) . This gives a direct route to the two unbroken gauge symmetries of the standard model. [ABSTRACT FROM AUTHOR]

We explore the performance of various correlation measures for open Dirac system with Hawking effect in Schwarzschild space–time. Our results indicate that the impact of Hawking effect on physical accessible entanglement is weaker than that of decoherence. For generalized amplitude damping (GAD) channel, the entanglement sudden death (ESD) is analyzed in detail, and the inequivalence of quantization for Dirac particles in the black hole and Kruskal space–time is verified via quantum discord measure. In addition, as an example for interpreting Bell non-locality, we study the GAD channel with Hawking effect. It can be noticed that there is a boundary line of Bell violation for physically accessible states. That is, quantum non-locality would disappear when Hawking temperature exceeds a certain value. This critical temperature increases as a decoherence parameter decreases. In the case of phase damping (PD) channel, the interaction between the particle and noise environment does not produce bipartite system–environment entanglement. Then we discuss entanglement distributions, and find that the reduced physically accessible entanglement can be redistributed to physical inaccessible region. At last, we extend our investigation to an N -qubit system, and obtain a universal expression of the physical accessible entanglement. [ABSTRACT FROM AUTHOR]

The BRST quantizations of worldsheet gravity corresponding to final more acceptable derivative gauge and the standard conformal gauge are studied. We establish a mapping between these two gauges utilizing FFBRST formulation in standard way. Therefore, we are able to declare that the problems associated with Virasoro constraints are the gauge artifact. [ABSTRACT FROM AUTHOR]

We show that a Nambu–Goto string has a nontrivial zero length limit which corresponds to a massless particle with extrinsic curvature. The system has the set of six first class constraints, which restrict the phase space variables so that the spin vanishes. Upon quantization, we obtain six conditions on the state, which can be represented as a wave function of position coordinates, x μ , and velocities, q μ . We have found a wave function ψ ( x , q ) that turns out to be a general solution of the corresponding system of six differential equations, if the dimensionality of spacetime is eight. Although classically the system is just a point particle with vanishing extrinsic curvature and spin, the quantized system is not trivial, because it is consistent in eight, but not in arbitrary, dimensions. [ABSTRACT FROM AUTHOR]

The combined considerations of both the bulk liquid-drop-type behavior and the quantized angular momentum reveal that high-spin toroidal isomeric states may have general occurrences for light nuclei with 28 ⩽ A ⩽ 52 . High-spin N = Z toroidal isomers in this mass region have been located theoretically using cranked self-consistent constraint Skyrme–Hartree–Fock model calculations. [ABSTRACT FROM AUTHOR]

Basis Light-front Quantization has been proposed as a nonperturbative framework for solving quantum field theory. We apply this approach to Quantum Electrodynamics and explicitly solve for the light-front wave function of a physical electron. Based on the resulting light-front wave function, we evaluate the electron anomalous magnetic moment. Nonperturbative mass renormalization is performed. Upon extrapolation to the infinite basis limit our numerical results agree with the Schwinger result obtained in perturbation theory to an accuracy of 0.06%. [ABSTRACT FROM AUTHOR]

We prescribe a formulation of the particle production with real-time Stochastic Quantization. To construct the retarded and the time-ordered propagators we decompose the stochastic variables into positive- and negative-energy parts. In this way we demonstrate how to derive a standard formula for the Schwinger mechanism under time-dependent electric fields. We discuss a mapping to the Schwinger-Keldysh formalism and a relation to the classical statistical simulation. [ABSTRACT FROM AUTHOR]

Abstract: We suggest a minimal extension of the standard model, which can explain current experimental data of the dark matter, small neutrino masses and baryon asymmetry of the universe, inflation, and dark energy, and achieve gauge coupling unification. The gauge coupling unification can explain the charge quantization, and be realized by introducing six new fields. We investigate the vacuum stability, coupling perturbativity, and correct dark matter abundance in this model by use of current experimental data. [Copyright &y& Elsevier]

Abstract: We investigate charge quantization in the Standard Model (SM) through a nonlinear sigma model (NLSM), , and a model, . We also generalize to any model. Charge quantization follows from the consistency and dynamics of the NLSM, without a monopole or Grand Unified Theory, as shown in our earlier work on the model (arXiv:1309.0692). We find that representations of the matter fields under the unbroken non-abelian subgroup dictate their charge quantization under the factor. In the model the unbroken group is identified with the weak and hypercharge groups of the SM, and the Nambu–Goldstone boson (NGB) has the quantum numbers of a SM Higgs. There is the intriguing possibility of a connection with the vanishing of the Higgs self-coupling at the Planck scale. Interestingly, with some minor assumptions (no vector-like matter and minimal representations) and starting with a single quark doublet, anomaly cancellation requires the matter structure of a generation in the SM. Similar analysis holds in the model, with the unbroken group identified with QCD and hypercharge, and the NGB having the up quark as a partner in a supersymmetric model. This can motivate solving the strong CP problem with a vanishing up quark mass. [Copyright &y& Elsevier]

Abstract: We investigate the consistency conditions for matter fields coupled to the four-dimensional ( supersymmetric) nonlinear sigma model (the coset space ). We find that consistency requires that the charge of the matter be quantized, in units of half of the charge of the Nambu–Goldstone (NG) boson, if the matter has a nonsingular kinetic term and the dynamics respect the full group . We can then take the linearly realized group to comprise the weak hypercharge group of the Standard Model. Thus we have charge quantization without a Grand Unified Theory (GUT), completely avoiding problems like proton decay, doublet–triplet splitting, and magnetic monopoles. We briefly investigate the phenomenological implications of this model-building framework. The NG boson is fractionally charged and completely stable. It can be naturally light, avoiding constraints while being a component of dark matter or having applications in nuclear physics. We also comment on the extension to other NLSMs on coset spaces, which will be explored more fully in a followup paper. [Copyright &y& Elsevier]

Abstract: We investigate the modification of the pion self-energy at finite temperature due to its interaction with a low-density, isospin-symmetric nuclear medium embedded in a constant magnetic background. To one loop, for fixed temperature and density, we find that the pion effective mass increases with the magnetic field. For the , interestingly, this happens solely due to the trivial Landau quantization shift , since the real part of the self-energy is negative in this case. In a scenario in which other charged particle species are present and undergo an analogous trivial shift, the relevant behavior of the effective mass might be determined essentially by the real part of the self-energy. In this case, we find that the pion mass decreases by for a magnetic field , which favors pion condensation at high density and low temperatures. [Copyright &y& Elsevier]

Abstract: In this Letter we will analyze the creation of the multiverse. We will first calculate the wave function for the multiverse using third quantization. Then we will fourth-quantize this theory. We will show that there is no single vacuum state for this theory. Thus, we can end up with a multiverse, even after starting from a vacuum state. This will be used as a possible explanation for the creation of the multiverse. We also analyze the effect of interactions in this fourth-quantized theory. [Copyright &y& Elsevier]

Abstract: There are two known approaches for quantizing the SU(2) Skyrme model, the semiclassical and canonical quantization. The semiclassical approach does not take into account the non-commutativity of velocity of quantum coordinates and the stability of the semiclassical soliton is conveniently ensured by the symmetry breaking term. The canonical quantum approach leads to quantum mass correction that is not obtained in the semiclassical approach. In this Letter we argue that these two approaches are not equivalent and lead to different results. We show that the resulting profile functions have the same asymptotic behaviour, however their shape in the region close to the origin is different. [Copyright &y& Elsevier]

Abstract: It is pointed out that the equations (and its super-symmetrizations, playing a central role in M-theory matrix models) describe non-commutative minimal surfaces – and can be solved as such. [Copyright &y& Elsevier]

Abstract: In this work we analyze a non-interacting one-dimensional polymer Bose–Einstein condensate in a harmonic trap within the semiclassical approximation. We use an effective Hamiltonian coming from the polymer quantization that arises in loop quantum gravity. We calculate the number of particles in order to obtain the critical temperature. The Bose–Einstein functions are replaced by series, whose high order terms are related to powers of the polymer length. It is shown that the condensation temperature presents a shift respect to the standard case, for small values of the polymer scale. In typical experimental conditions, it is possible to establish a bound for up to . To improve this bound we should decrease the frequency of the trap and also decrease the number of particles. [Copyright &y& Elsevier]

Abstract: Lattice radial quantization is introduced as a nonperturbative method intended to numerically solve Euclidean conformal field theories that can be realized as fixed points of known Lagrangians. As an example, we employ a lattice shaped as a cylinder with a 2D Icosahedral cross-section to discretize dilatations in the 3D Ising model. Using the integer spacing of the anomalous dimensions of the first two descendants ( ), we obtain an estimate for . We also observed small deviations from integer spacing for the 3rd descendant, which suggests that a further improvement of our radial lattice action will be required to guarantee conformal symmetry at the Wilson–Fisher fixed point in the continuum limit. [Copyright &y& Elsevier]

Abstract: The quantization of non-Abelian gauge theories is known to be plagued by Gribov copies. Typical examples are the copies related to zero modes of the Faddeev–Popov operator, which give rise to singularities in the ghost propagator. In this work we present an exact and compact expression for the ghost propagator as a function of external gauge fields, in Yang–Mills theory in the Landau gauge. It is shown, to all orders, that the condition for the ghost propagator not to have a pole, the so-called Gribovʼs no-pole condition, can be implemented by demanding a non-vanishing expectation value for a functional of the gauge fields that turns out to be Zwanzigerʼs horizon function. The action allowing to implement this condition is the Gribov–Zwanziger action. This establishes in a precise way the equivalence between Gribovʼs no-pole condition and Zwanzigerʼs horizon condition. [Copyright &y& Elsevier]

Abstract: Time operator is studied on the basis of field quantization, where the difficulty stemming from Pauliʼs theorem is circumvented by borrowing ideas from the covariant quantization of the bosonic string, i.e., one can remove the negative energy states by imposing Virasoro constraints. Applying the index theorem, one can show that in a different subspace of a Fock space, there is a different self-adjoint time operator. However, the self-adjoint time operator in the maximal subspace of the Fock space can also represent the self-adjoint time operator in the other subspaces, such that it can be taken as the single, universal time operator. Furthermore, a new insight on Pauliʼs theorem is presented. [Copyright &y& Elsevier]

Abstract: It is well known that coupling a spin- field to a gravitational or electromagnetic background leads to potential problems both in the classical and in the quantum theory. Various solutions to these problems have been proposed so far, which are all restricted to a limited class of backgrounds. On the other hand, negative results for general gravitational backgrounds have been reported only for a limited set of couplings to the background to date. Hence, to our knowledge, a comprehensive analysis of all possible couplings to the gravitational field and general gravitational backgrounds including off-shell ones has not been performed so far. In this work we analyse whether it is possible to couple a spin- field to a gravitational field in such a way that the resulting quantum theory is consistent on arbitrary gravitational backgrounds. We find that this is impossible as all couplings require the background to be an Einstein spacetime for consistency. This enforces the widespread belief that supergravity theories are the only meaningful models which contain spin- fields as in these models such restrictions of the gravitational background appear naturally as on-shell conditions. [Copyright &y& Elsevier]