Search

We use the noncommutative Higgs effective standard model to make a phenomenological prediction for the transverse momentum distribution of the Higgs boson produced in association with a jet at hadron colliders. We calculate at leading order in the noncommutative parameter Θ as well as leading order in the strong coupling α s , the one-loop p t distribution of the Higgs boson. As in the standard model, the fixed-order distribution suffers from large logarithms at small p t which require an all-orders resummation. We find that the large- p t region of the distribution is strongly affected by the non-commutativity, while small- p t region is not. Following this observation, we propose a simple matching method that allows us to compute a result that is also valid at small p t obtained with standard-model parton showers such as Pythia 8. We also compare our results with the next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) distributions in the standard model, in order to assess the importance of higher-order effects in the search for non-commutativity at colliders. [ABSTRACT FROM AUTHOR]

In this paper, within the framework of relativistic quantum mechanics and using the improved approximation scheme to the centrifugal term for any l states via Bopp's shift method and standard perturbation theory, we have obtained the modified energy eigenvalues of a newly proposed modified unequal vector and scalar Hellmann plus modified Kratzer potentials (DUVSHMK-Ps) for some diatomic N2, I2, CO, NO, O2 and HCl molecules. This study includes corrections of the first-order in noncommutativity parameters (Θ , σ). This potential is a superposition of the attractive Coulomb Yukawa potential plus the Kratzer potential and new central terms appear as a result of the effects of noncommutativity properties of space–space. The obtained energy eigenvalues appear as a function of noncommutativity parameters, the strength parameters (V 0 , S 0) and (V 1 , S 1) of the (scalar vector) Hellmann potential, the screening range parameter α , the dissociation energy of the vector, and scalar potential (D v , D s) , the equilibrium inter-nuclear distance r e in addition to the atomic quantum numbers (n , j , l , s , m). Furthermore, we obtained the corresponding modified energy of DUVSHMK-Ps in the symmetries of non-relativistic noncommutative quantum mechanics (NRNCQM). In both relativistic and non-relativistic problems, we show that the corrections on the spectrum energy are smaller than the main energy in the ordinary cases of RQM and NRQM. [ABSTRACT FROM AUTHOR]

We discuss the corrections to the orbital period of a particle in a constant magnetic field, driven by the model of noncommutative geometry recently associated to a quantum clock. The effects are extremely small, but in principle detectable. [ABSTRACT FROM AUTHOR]

Noncommutative geometry, an offshoot of string theory, replaces point-like objects by smeared objects. The resulting uncertainty may cause a black hole to be observationally indistinguishable from a traversable wormhole, while the latter, in turn, may become observationally indistinguishable from a gravastar. The same noncommutative-geometry background allows the theoretical construction of thin-shell wormholes from gravastars and may even serve as a model for dark energy. [ABSTRACT FROM AUTHOR]

We consider the 𝒫 𝒯 -symmetric quantum field theory on the noncommutative spacetime with angular twist and construct its pseudo-Hermitian interpretation. We explore the differences between internal and spatial parities in the context of the angular twist and for the latter we find new 𝒫 𝒯 -symmetric interactions that are nontrivial only for the noncommutative spacetime. We reproduce the same formula for the leading order T-matrix of the equivalent Hermitian model as the one obtained earlier for the quantum field theory on the commutative spacetime. This formula implies that the leading order scattering amplitude preserves the symmetries of the noncommutative geometry if they are not broken in the non-Hermitian formulation. [ABSTRACT FROM AUTHOR]

In this paper, we provide five canonical and three Lie-algebraic twist-deformations of Carroll, para-Galilei and Static Hopf algebras. Particularly, in the case of Carroll Hopf structure, we get the same result with the use of contraction schemes of corresponding canonically and Lie-algebraically twisted Poincaré Hopf algebras as well. [ABSTRACT FROM AUTHOR]

Discretized Kaluza-Klein theory in spacetime can be constructed based on the concepts of noncommutative geometry. In this paper, we show that it is possible to incorporate the non-Abelian gauge fields in this framework. The generalized Hilbert-Einstein action is gauge invariant only in two cases. In the first case, the gauge group must be Abelian on one sheet of spacetime and non-Abelian on the other one. In the second case, the gauge group must be the same on two sheets of spacetime. Actually, the theories of electroweak and strong interactions can fit into these two cases. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of static spherically symmetric wormhole solutions along with noncommutative geometry in the background of F( T, T) gravity. We assume a nonzero redshift function as well as two well-known models of this gravity and discuss the behavior of null/weak energy conditions graphically. We conclude that there does not exist any physically acceptable wormhole solution for the first model, but there is a chance to develop physically acceptable wormhole solution in a particular region for the second model. [ABSTRACT FROM AUTHOR]

We make biframe and quaternion extensions on the noncommutative geometry, and construct the biframe spacetime for the unification of gravity and quantum field theory (QFT). The extended geometry distinguishes between the ordinary spacetime based on the frame bundle and an extra non-coordinate spacetime based on the biframe bundle constructed by our extensions. The ordinary spacetime frame is globally flat and plays the role as the spacetime frame in which the fields of the Standard Model are defined. The non-coordinate frame is locally flat and is the gravity spacetime frame. The field defined in both frames of such 'flat' biframe spacetime can be quantized and plays the role as the gravity field which couples with all the fields to connect the gravity effect with the Standard Model. Thus, we provide a geometric paradigm in which gravity and QFT can be unified. [ABSTRACT FROM AUTHOR]

We discuss a possible interpretation of the 750 GeV diphoton resonance, recently reported at the large hadron collider (LHC), within a class of models with gauge coupling unification. The unification is imposed by the underlying noncommutative geometry (NCG), which in these models is extended to a left-right symmetric completion of the Standard Model (SM). Within such unified models the Higgs content is restrictively determined from the underlying NCG, instead of being arbitrarily selected. We show that the observed cross-sections involving the 750 GeV diphoton resonance could be realized through a SM singlet scalar field accompanied by colored scalars, present in these unified models. In view of this result, we discuss the underlying rigidity of these models in the NCG framework and the wider implications of the NCG approach for physics beyond the SM. [ABSTRACT FROM AUTHOR]

In this paper, we study noncommutative static spherically symmetric wormhole solutions in the context of modified Gauss-Bonnet gravity. We explore these solutions either by assuming a viable model to construct shape function or by specifying the shape function to deduce model. The energy conditions are discussed for both types of wormholes. In the first case, we find a physically acceptable wormhole solution threaded by normal matter for all values of radial coordinate while the second case gives physical solution only for large values of . [ABSTRACT FROM AUTHOR]

We analyze the *-product induced on, F(R3) by a suitable reduction of the Moyal product defined on F(R4) This is obtained through the identification R3≃ g*, with ga three-dimensional Lie algebra. We consider the su(2) case, exhibit a matrix basis and realize the algebra of functions on su(2)* in such a basis. The relation to the Duflo map is discussed. As an application to quantum mechanics we compute the spectrum of the hydrogen atom [ABSTRACT FROM AUTHOR]

We review some aspects of quantum gravity in the context of cosmology. In particular, we focus on models with a phenomenology accessible to current and near-future observations, as the early Universe might be our only chance to peep through the quantum gravity realm. [ABSTRACT FROM AUTHOR]

A unifying perspective on the Moyal and Voros products and their physical meanings has been recently presented in the literature, where the Voros formulation admits a consistent physical interpretation. We define a star product ⋆, in terms of an antisymmetric fixed matrix Θ, and an arbitrary symmetric matrix Φ, that is a generalization of the Moyal and the Voros products. We discuss the quantum mechanics and the physical meaning of the generalized star product. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to use the idea in J. Geom. Phys.42, 54 (2002) to compute the topological charges for a (finite) sequence of noncommutative line bundles over the fuzzy sphere. Central to this task is to construct projective modules associated with sequence of the irreducible sub-representations of the tensor product of two different irreps of SU(2). The topological charges corresponding to such fuzzy line bundles are fractional and different from each other. However, in the commutative limit, those tend to Chern numbers of a sequence of the complex line bundles over two-sphere. [ABSTRACT FROM AUTHOR]

We construct a Dirac equation in κ-Minkowski spacetime and analyze its implications. This κ-deformed Dirac equation is expanded as a power series involving derivatives with respect to commutative coordinates and the deformation parameter, a. We show that the κ-deformation breaks the charge conjugation invariance but preserves parity and time reversal. We then study how the hydrogen atom spectrum is modified due to the κ-deformation, applying perturbation theory. Using this, we obtain bounds on the deformation parameter a, which are a few orders higher than the Planck length. We also show that the effects of deformation on the spectrum are distinct from that of Moyal deformation and generalized uncertainty principle. [ABSTRACT FROM AUTHOR]

In this paper, we construct a model of spinor fields interacting with specific gauge fields on the fuzzy sphere and analyze the chiral symmetry of this "Schwinger model". In constructing the theory of gauge fields interacting with spinors on the fuzzy sphere, we take the approach that the Dirac operator Dq on the q-deformed fuzzy sphere $S_{qF}^2$ is the gauged Dirac operator on the fuzzy sphere. This introduces interaction between spinors and specific one-parameter family of gauge fields. We also show how to express the field strength for this gauge field in terms of the Dirac operators Dq and D alone. Using the path integral method, we have calculated the 2n-point functions of this model and show that, in general, they do not vanish, reflecting the chiral non-invariance of the partition function. [ABSTRACT FROM AUTHOR]

We study the modification of Newton's second law, upto first order in the deformation parameter a, in the κ-spacetime. We derive the deformed Hamiltonian, expressed in terms of the commutative phase space variables, describing the particle moving in a central potential in the κ-spacetime. Using this, we find the modified equations of motion and show that there is an additional force along the radial direction. Using Pioneer anomaly data, we set a bound for a. We also analyze the violation of equivalence principle predicted by the modified Newton's equation, valid up to first order in a and use this also to set an upper bound on a. [ABSTRACT FROM AUTHOR]

We show that vortices of Yang–Mills–Higgs model in R2 space can be regarded as instantons of Yang–Mills model in R2 × Z2 space. For this, we construct the noncommutative Z2 space by explicitly fixing the Z2 coordinates and then show, by using the Z2 coordinates, that BPS equation for the vortices can be considered as a self-dual equation. We also propose the possibility to rewrite the BPS equations for vortices as ADHM equations through the use of self-dual equation. [ABSTRACT FROM AUTHOR]

We study and analyse the questions regarding breakdown of global symmetry on noncommutative sphere. We demonstrate this by considering a complex scalar field on a fuzzy sphere and isolating Goldstone modes. We discuss the role of nonlocal interactions present in these through geometrical considerations. [ABSTRACT FROM AUTHOR]

In this note we extend the methods developed by Freidel et al.20 to derive the form of ϕ4 interaction term in the case of scalar field theory on κ-Minkowski space, defined in terms of star product. We present explicit expressions for the κ-Minkowski star product. Having obtained the the interaction term we use the resulting deformed conservation rules to investigate if they lead to any threshold anomaly, and we find that in the leading order they do not, as expected. [ABSTRACT FROM AUTHOR]

We show how to get a noncommutative product for functions on spacetime starting from the deformation of the coproduct of the Poincaré group using the Drinfel'd twist. Thus it is easy to see that the commutative algebra of functions on spacetime (ℝ4) can be identified as the set of functions on the Poincaré group invariant under the right action of the Lorentz group provided we use the standard coproduct for the Poincaré group. We obtain our results for the noncommutative Moyal plane by generalizing this result to the case of the twisted coproduct. This extension is not trivial and involves cohomological features. As is known, spacetime algebra fixes the coproduct on the diffeomorphism group of the manifold. We now see that the influence is reciprocal: they are strongly tied. [ABSTRACT FROM AUTHOR]

The Moyal and Wick–Voros planes $\mathcal{A}_{\theta}^{\mathcal{M}},V$ are *-isomorphic. On each of these planes the Poincaré group acts as a Hopf algebra symmetry if its coproducts are deformed by twist factors $F_{\theta}^{\mathcal{M},V}$. We show that the *-isomorphism ${\rm T}$: $\mathcal{A}_{\theta}^{\mathcal{M}}to\mathcal{A}_{\theta}$ also does not map the corresponding twists of the Poincaré group algebra. The quantum field theories on these planes with twisted Poincaré–Hopf symmetries are thus inequivalent. We explicitly verify this result by showing that a nontrivial dependence on the noncommutative parameter is present for the Wick–Voros plane in a self-energy diagram whereas it is known to be absent on the Moyal plane (in the absence of gauge fields).1–3 Our results differ from those of Ref. 4 because of differences in the treatments of quantum field theories. [ABSTRACT FROM AUTHOR]

We present a procedure to evaluate the action for dielectric branes in nontrivial backgrounds. These backgrounds must be capable to be taken into a Kaluza–Klein form, with some nonzero wrapping factor. We derive the way this wrapping factor is gauged away. Examples of this are AdS5 × S5 and AdS3 × S3 × T4, where we perform the construction of different stable systems, which stability relies in its dielectric character. [ABSTRACT FROM AUTHOR]

Models of particle physics with Noncommutative Geometry (NCG) generally suffer from a manifestly non-Wilsonian coupling of infrared and ultraviolet degrees of freedom known as the "IR/UV Problem" which would tend to compromise their phenomenological relevance. In this letter we explicitly show how one may remedy this by coupling NCG to gravity. In the simplest scenario, the Lagrangian gets multiplied by a nonconstant background metric; in ϕ-4 theory the theorem that ∫ d4x ϕ⋆ϕ=∫ d4x ϕ2 is no longer true and the field propagator gets modified by a factor which depends on both NCG and the variation of the metric. A suitable limit of this factor as the propagating momentum gets asymptotically large then eradicates the IR/UV problem. With gravity and NCG coupled to each other, one might expect antisymmetric components to arise in the metric. Cosmological implications of such are subsequently discussed. [ABSTRACT FROM AUTHOR]

We discuss conformal symmetry on the two-dimensional noncommutative plane equipped with Moyal product in the twist deformed context. We show that the consistent use of the twist procedure leads to results which are free from ambiguities. This lends support to the importance of the use of twist symmetries in noncommutative geometry. [ABSTRACT FROM AUTHOR]

We investigate the effects of space noncommutativity and the generalized uncertainty principle on the thermodynamics of a radiating Schwarzschild black hole. We show that evaporation process is in such a way that black hole reaches a maximum temperature before its final stage of evolution and then cools down to a nonsingular remnant with zero temperature and entropy. We compare our results with more reliable results of string theory. This comparison shows that GUP and space noncommutativity are similar concepts at least from the viewpoint of black hole thermodynamics. [ABSTRACT FROM AUTHOR]

A quantum analogue of SL(2) covariance is given. The method consists of defining a bilinear form on SLq(2) co-module, then we ask the defined form to be invariant under SLq(2) co-actions. We showed that the required invariance leads to the standard algebraic structure of SLq(2) ideal. On the other hand, the geometry of the three-dimensional quantum Euclidean space has been evoked by computing the quantum Euclidean metric, the quantum Euclidean "distance" (the central element) and the relation of orthogonality of SOq(3) quantum group. [ABSTRACT FROM AUTHOR]

Lorentz invariant supersymmetric deformations of superspaces based on Moyal star product parametrized by Majorana spinor λa and Ramond Grassmannian vector $\psi_{m}=-{1\over 2}(\bar\theta\gamma_{m}\lambda)$ in the spinor realization42 are proposed. The map of supergravity background into composite supercoordinates: $(B^{-1}_{mn}, \Psi^{a}_{m}, C_{ab}) \leftrightarrow (i\psi_{m}\psi_{n}, \psi_{m}\lambda^{a}, \lambda_{a}\lambda_{b})$ valid up to the second order corrections in deformation parameter h and transforming the background dependent Lorentz noninvariant (anti)commutators of supercoordinates into their invariant Moyal brackets is revealed. We found one of the deformations to depend on the axial vector $\psi_{1m}=\frac{1}{2}(\bar\theta\gamma_{m}\gamma_{5}\lambda)$ and to vanish for the θ components with the same chiralities. The deformations in the (super)twistor picture are discussed. [ABSTRACT FROM AUTHOR]

We study noncommutative field theories, which are inherently nonlocal, using a Poincaré-invariant regularisation scheme which yields an effective, nonlocal theory for energies below a cutoff scale. After discussing the general features and the peculiar advantages of this regularisation scheme for theories defined in noncommutative spaces, we focus our attention on the particular case when the noncommutativity parameter is inversely proportional to the square of the cutoff, via a dimensionless parameter η. We work out the perturbative corrections at one-loop order for a scalar theory with quartic interactions, where the signature of noncommutativity appears in η-dependent terms. The implications of this approach, which avoids the problems related to uv–ir mixing, are discussed from the perspective of the Wilson renormalisation program. Finally, we remark about the generality of the method, arguing that it may lead to phenomenologically relevant predictions, when applied to realistic field theories. [ABSTRACT FROM AUTHOR]

By considering a new form of dimensional reduction for noncommutative field theory, we show that the signature of spacetime may be changed. In particular, it is demonstrated that a temporal dimension can emerge from a purely Euclidean geometry. We suggest that this mechanism may hint at the origin of time in the fundamental theory of quantum gravity. [ABSTRACT FROM AUTHOR]

We explore the consequences of time-space noncommutativity in the quantum mechanics of atoms and molecules, focusing on the Moyal plane with just time-space noncommutativity $([\hat{x}_\mu,\hat{x}_\nu]=i\theta_{\mu\nu}, \theta_{0i}\neq 0, \theta_{ij}=0)$. Space rotations and parity are not automorphisms of this algebra and are not symmetries of quantum physics. Still, when there are spectral degeneracies of a time-independent Hamiltonian on a commutative spacetime which are due to symmetries, they persist when θ0i≠0: they do not depend at all on θ0i. They give no clue about rotation and parity violation when θ0i≠0. The persistence of degeneracies for θ0i≠0 can be understood in terms of invariance under deformed noncommutative "rotations" and "parity". They are not spatial rotations and reflection. We explain such deformed symmetries. We emphasize the significance of time-dependent perturbations (for example, due to time-dependent electromagnetic fields) to observe noncommutativity. The formalism for treating transition processes is illustrated by the example of nonrelativistic hydrogen atom interacting with quantized electromagnetic field. In the tree approximation, the 2s→1s + γ transition for hydrogen is zero in the commutative case. As an example, we show that it is zero in the same approximation for θ0i≠0. The importance of the deformed rotational symmetry is commented upon further using the decay Z0→2γ as an example. [ABSTRACT FROM AUTHOR]

We propose a simple low-energy classical experiment in which the effects of noncommutativity can be clearly separated from commutative physics. The ensuing bound on the noncommutative scale is remarkable, especially in view of its elementary derivation. [ABSTRACT FROM AUTHOR]

We give a brief account of the description of the standard model in noncommutative geometry as well as the thermal time hypothesis, questioning their relevance for quantum gravity. [ABSTRACT FROM AUTHOR]

A model for noncommutative scalar fields coupled to gravity based on the generalization of the Moyal product is proposed. Solutions compatible with homogeneous and isotropic flat Robertson-Walker spaces to first non-trivial order in the perturbation of the star-product are presented. It is shown that in the context of a typical chaotic inflationary scenario, at least in the slow-roll regime, noncommutativity yields no observable effect. [ABSTRACT FROM AUTHOR]

We argue that the model of a quantum computer with N qubits on a quantum space background, which is a fuzzy sphere with n = 2N elementary cells, can be viewed as the minimal model for quantum gravity. In fact, it is discrete, has no free parameters, is Lorentz-invariant, naturally realizes the holographic principle, and defines a subset of punctures of spin networks' edges of loop quantum gravity labelled by spins j = 2N-1-½. In this model, the discrete area spectrum of the cells, which is not equally spaced, is given in units of the minimal area of loop quantum gravity (for j = 1/2), and provides a discrete emission spectrum for quantum black holes. When the black hole emits one string of N bits encoded in one of the n cells, its horizon area decreases of an amount equal to the area of one cell. [ABSTRACT FROM AUTHOR]

Noncommutative corrections to the MIC–Kepler system (i.e. hydrogen atom in the presence of a magnetic monopole) are computed in Cartesian and spherical coordinates. In the framework of perturbation theory we were able to derive noncommutative corrections to the MIC–Kepler spectrum. We also found a nontrivial contribution to the linear Stark effect which did not exist in the standard hydrogen model. [ABSTRACT FROM AUTHOR]

It is argued that the internal dynamics of a baryon, as a bound state of QCD-strings and quarks, may be captured by a theory of matrix coordinates. [ABSTRACT FROM AUTHOR]

We study σ-models on noncommutative spaces, notably on noncommutative tori. We construct instanton solutions carrying a nontrivial topological charge q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons is conjectured to consists of an ordinary torus endowed with a complex structure times a projective space [formula]. [ABSTRACT FROM AUTHOR]

We present a brief review of the fuzzy disc, the finite algebra approximating functions on a disc, which we have introduced earlier. We also present a comparison with recent papers of Balachandran, Gupta and Kürkçüoǧlu, and of Pinzul and Stern, aimed at the discussion of edge states of a Chern-Simons thoery. [ABSTRACT FROM AUTHOR]

We use the framework of noncommutative geometry to define a discrete model for fluctuating geometry. Instead of considering ordinary geometry and its metric fluctuations, we consider generalized geometries where topology and dimension can also fluctuate. The model describes the geometry of spaces with a countable number n of points. The spectral principle of Connes and Chamseddine is used to define dynamics. We show that this simple model has two phases. The expectation value 〈n〉, the average number of points in the universe, is finite in one phase and diverges in the other. Moreover, the dimension δ is a dynamical observable in our model, and plays the role of an order parameter. The computation of 〈δ〉 is discussed and an upper bound is found, 〈δ〉 < 2. We also address another discrete model defined on a fixed d = 1 dimension, where topology fluctuates. We comment on a possible spontaneous localization of topology. [ABSTRACT FROM AUTHOR]

We improve the study of the lack of perturbative unitarity of noncommutative space-time quantum field theories derived from open string theory in electric backgrounds, enforcing the universality of the mechanism by which a tachyonic branch cut appears when the Seiberg-Witten limit freezes the string in an unstable vacuum. The main example is realized in the context of the on-shell four-tachyon amplitude of the bosonic string, and the dependence of the phenomenon on the brane-worldvolume dimension is analysed. We discuss the possibility of a proof in superstring theory, and finally mention the NCOS limit in this framework. [ABSTRACT FROM AUTHOR]

We analytically calculate the topological charge of general noncommutative U (N) instantons using the Corrigan's identity and find that the result is exactly the instanton number k, which appears in the noncommutative ADHM construction as the dimension of the vector space V. This result coincides with the corresponding fact in the commutative case. [ABSTRACT FROM AUTHOR]

We have calculated the topological charge of U(N) instantons on nondegenerate noncommutative spacetime to be exactly the instanton number k in a previous paper.1 This paper, which deals with the degenerate ${\bf R}^2_{\rm NC}\times{\bf R}^2$ case, is the continuation of Ref. 1. We find that the same conclusion holds in this case, thus complete the answer to the problem of topological charge of noncommutative U(N) instantons. [ABSTRACT FROM AUTHOR]