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Lie–Poisson gauge formalism provides a semiclassical description of noncommutative U(1) gauge theory with Lie algebra type noncommutativity. Using the Dirac approach to constrained Hamiltonian systems, we focus on a class of Lie–Poisson gauge models, which exhibit an admissible Lagrangian description. The underlying noncommutativity is supposed to be purely spatial. Analyzing the constraints, we demonstrate that these models have as many physical degrees of freedom as there are present in the Maxwell theory. [ABSTRACT FROM AUTHOR]

In this paper, we discuss exact realizations of the Yang–Poisson model on canonical phase space. The Yang model is an example of noncommutative geometry on a background space–time of constant curvature and is notable for its duality between position and momentum manifolds. We call Yang–Poisson model its classical limit, with commutators replaced by Poisson brackets. The structure is simpler in the classical case, and exact realizations can be found. [ABSTRACT FROM AUTHOR]

We study a noncommutative (NC) deformation of a charged scalar field, minimally coupled to a classical (commutative) Reissner–Nordström-like background. The deformation is performed via a particularly chosen Killing twist to ensure that the geometry remains undeformed (commutative). An action describing a NC scalar field minimally coupled to the RN geometry is manifestly invariant under the deformed U (1) ⋆ gauge symmetry. We find the equation of motion and conclude that the same equation is obtained from the commutative theory in a modified geometrical background described by an effective metric. This correspondence we call "duality between formal and effective approach". We also show that a NC deformation via semi-Killing twist operator cannot be rewritten in terms of an effective metric. There is dual description for those particular deformations. [ABSTRACT FROM AUTHOR]

In this contribution, we summarize our recent studies of the phase structure of the Grosse–Wulkenhaar model and its connection to renormalizability. Its action contains a special term that couples the field to the curvature of the noncommutative background space. We first analyze the numerically obtained phase diagram of the model and its three phases: the ordered, the disordered, and the noncommutative stripe phase. Afterward, we discuss the analytical derivation of the effective action and the ordered-to-stripe transition line, and how the obtained expression successfully explains the curvature-induced shift of the triple point compared to the model without curvature. This shift also causes the removal of the stripe phase and makes the model renormalizable. [ABSTRACT FROM AUTHOR]

Relativistic and nonrelativistic quantum mechanics formulated in a noncommutative space–space have recently become the object of renewed interest. In the context of three-dimensional extended relativistic quantum mechanics (3D-ERQM) symmetries with arbitrary spin-orbit coupling quantum number k , we approximate to solve the deformed Dirac equation for a new suggested new generalized Morse potential and a class of Yukawa potential including improved Coulomb-like tensor interaction (N(GMP-CYP) plus ICLTI). In the framework of the spin and pseudospin (p-spin) symmetry, we obtain the global new energy eigenvalue which equals the energy eigenvalue in the usual relativistic QM as the main part plus three corrected parts produced from the effect of the spin-orbit interaction, the new modified Zeeman, and the rotational Fermi term, by using the parametric of the well-known Bopp's shift method and standard perturbation theory using Greene–Aldrich approximation to nonlinear and exponential terms in the effective potential. The new values that we got appeared sensitive to the quantum numbers (j , k , l / l ̃ , s / s ̃ , m / m ̃), the mixed potential depths ( D e , r e , a , b , c), the range of the potential α and noncommutativity parameters (Θ , τ , χ). We have studied the nonrelativistic limit of new spin symmetry under the N(GMP-ICYP) model, we will also treat some important special cases such as the new generalized Morse potential, the new class of Yukawa potential, the new Hellmann potential, the new inversely quadratic Yukawa potential, the new Hulthén potential and new Coulomb potential. Finally, we studied a case of composite systems. [ABSTRACT FROM AUTHOR]

The main findings of the generalized uncertainty principle (GUP), the phenomenological approach, for instance, the emergence of a minimal measurable length uncertainty, are obtained in various versions from theories of quantum gravity, such as string theory, loop quantum gravity, doubly special relativity and black hole physics. GUP counts for impacts of relativistic energies and finite gravitational fields on the fundamental theories of quantum mechanics (QM), the noncommutation and measurement uncertainty. Utilizing GUP in reconciling principles of general relativity (GR) and QM, thereby enables to draw convincing conclusions about quantum gravity. To resolve the shortcuts reported with the nonrelativistic three-dimensional GUP, namely, violation of Lorentz covariance, dependence on frame of reference, and violation of the linear additional law of momenta, we introduce relativistic four-dimensional generalized uncertainty principle (RGUP) to curved spacetime. To unify GR and QM, we apply the Born reciprocity principle (BRP), distance-momentum duality symmetry and RGUP to estimate the fundamental tensor in discretized curved spacetime. To this end, we generalize Riemann geometry. The Finsler geometry, which is characterized by manifold and Finsler structure, allows to directly apply RGUP to the Finsler structure of a free particle so that F ( x ̂ 0 , ẋ 0) can be expressed as F ( x ̂ 0 , ϕ ̂ p ̂ 0) , from which the metric tensor in discretized Riemann spacetime could be deduced. We conclude that F ( x ̂ 0 , ϕ ̂ p ̂ 0) is homogeneous with degree 1 in p ̂ 0 , while ϕ ̂ = 1 + β 1 p ̂ 0 ρ p ̂ 0 ρ is 0 -homogeneous resulting in g ̃ μ ν ≃ (+ 2 β 1 F 2) [ 1 + m ̄ 2 | ẍ ̂ | 2 ] g μ ν . Despite, the astonishing similarity with the conformal transformation, know as Weyl tensor, this study suggests that principles of QMs could be unambiguously imposed on the resulting fundamental tensor. Also, we conclude that the features of Finsler geometry assumed in this study are likely the ones of the duel Hamilton geometry. [ABSTRACT FROM AUTHOR]

We construct the novel Clifford-Yang algebra which is an extension of the Yang algebra in noncommutative phase spaces. The Clifford-Yang algebra allows us to write down the commutators of the n o n c o m m u t a t i v e polyvector-valued coordinates and momenta which are compatible with the Jacobi identities, the Weyl–Heisenberg algebra, and paves the way for a formulation of quantum mechanics (QM) in noncommutative Clifford spaces. We continue with a detailed study of the isotropic 3D quantum oscillator in noncommutative spaces and find the energy eigenvalues and eigenfunctions. These findings differ considerably from the ordinary quantum oscillator in commutative spaces. We find that QM in noncommutative spaces leads to very different solutions, eigenvalues, and uncertainty relations than ordinary QM in commutative spaces. The generalization of QM to noncommutative Clifford (phase) spaces is attained via the Clifford-Yang algebra. The operators are now given by the generalized angular momentum operators involving polyvector coordinates and momenta. The eigenfunctions (wave functions) are now more complicated functions of the polyvector coordinates. We conclude with some important remarks. [ABSTRACT FROM AUTHOR]

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]

Relativistic and nonrelativistic quantum mechanics formulated in a noncommutative space-space have recently become the object of renewed interest. In the context of extended relativistic quantum mechanics (ERQM) symmetries with arbitrary spin-orbit coupling quantum number k , we approximate to solve the deformed Dirac equation (DDE) for a new suggested new generalized Schiöberg and Manning–Rosen potentials within the generalized (Coulomb and Yukawa)-like tensor interactions (NGSM-GLTs). In the framework of the spin and pseudospin (p-spin) symmetry, we obtain the global new energy eigenvalue which equals the energy eigenvalue in usual relativistic quantum mechanics (RQM) as the main part plus three corrected parts produced from the effect of the spin-orbit interaction, the new modified Zeeman, and the rotational Fermi term, by using the parametric of the well-known Bopp's shift method and standard perturbation theory using Greene–Aldrich approximation to handle 1 / r , 1 / r 2 and other terms in the effective potential. The new values that we got appeared sensitive to the quantum numbers (j , k , l / l ̃ , s / s ̃ , m / m ̃), the mixed potential depths ( D 0 , D 1 , σ , α , A), the range of the potential δ , and noncommutativity parameters (Θ , τ , χ). We recovered several potentials, including the improved Schiöberg and Manning–Rosen potentials within the improved Yukawa-like tensor interaction, the new Schiöberg and Manning–Rosen potentials within the improved Coulomb-like tensor interaction, the new Schiöberg potential within the improved Yukawa-like tensor interaction, the new Manning–Rosen potential within the improved Yukawa-like tensor interaction, and the new Schiöberg and Manning–Rosen potentials potential problems in the context of nonrelativistic extended quantum mechanics symmetries. [ABSTRACT FROM AUTHOR]

The Wilsonian renormalization group approach to matrix models is outlined and applied to multitrace matrix models with an emphasis on the computation of the fixed points which could describe the phase structure of noncommutative scalar phi-four theory. [ABSTRACT FROM AUTHOR]

In this paper, the wormholes have been constructed in the framework of the linear f (R , T) gravity model with noncommutative geometry. The wormhole solutions are obtained in the context of Gaussian and Lorentzian distributions of matter using f (R , T) gravity. The energy conditions such as null, weak, strong, and dominant energy conditions are explored and the regions satisfying these conditions are examined for both forms of matter distributions. Further, the stability of wormhole solutions is studied with the help of TOV (Tolman–Oppenheimer–Volkoff) equations. It is found that the wormhole solutions are stable and free from exotic matter for the suitable choice of parameters. [ABSTRACT FROM AUTHOR]

In this work, we considered analytical approximate bound state solutions of the mass-dependent deformed Dirac equation with the improved vector Eckart potential including the Yukawa tensor interaction (IEPDMYI for short) in the context of extended relativistic quantum mechanics ERQM symmetries. The new relativistic energy spectra of the DDE for the IEPDMYI with spin symmetry and pseudospin symmetry are obtained. The solutions for arbitrary k-wave are obtained by using the basic concept of Bopp's shift approach and standard perturbation by applying an approximation to the centrifugal-like term in the calculations. The new values that we get appeared sensitive to the discrete quantum numbers (j , k , l , l ̃ , s , s ̃ , m , m ̃) , the mixed potential depths (V 1 , V 2 , V 0) , the range of the potential α and noncommutativity parameters (Θ , σ , χ). We have highlighted three physical phenomena that automatically generate a result of the topological properties of noncommutativity, the first physical phenomena are the perturbative spin-orbit coupling, the second is the magnetic induction while the third corresponds to the rotational proper phenomena. We show that the corrections on the spectrum energy are smaller than the main energy in the usual cases of quantum field theory. In the ERQM symmetries, it is not possible to get the exact analytical solutions for (k = 0 , − 1 , + 1) , only the approximate solutions are available. We have obtained the energy equation for several well-known potentials by choosing appropriate parameters in the improved Eckart potential model such as the improved Hulthén potential and the improved generalized Morse potential. [ABSTRACT FROM AUTHOR]

The near-horizon noncommutative geometry of black holes, given by AdS 2 × N 2 , is discussed and the phase structure of the corresponding Yang–Mills matrix models is presented. The dominant phase transition as the system cools down, i.e. as the gauge coupling constant is decreased is an emergent geometry transition between a geometric noncommutative AdS 2 × N 2 phase (discrete spectrum) and a Yang–Mills matrix phase (continuous spectrum) with no background geometrical structure. We also find a possibility for topology change transitions in which space or time directions grow or decay as the temperature is varied. Indeed, the noncommutative near-horizon geometry AdS 2 × N 2 can evaporate only partially to a fuzzy sphere N 2 (emergence of time) or to a noncommutative anti-de Sitter space–time AdS 2 (topology change). [ABSTRACT FROM AUTHOR]

In this paper, we present the construction of noncommutative AdS 2 black hole and its four-dimensional Yang–Mills IKKT-type matrix model which includes two competing Myers term one responsible for the condensation of pure AdS 2 and the other one responsible for the condensation of the dilaton field. It is argued that the phase diagram of this matrix model features three phases: (1) a gravitational phase ( AdS 2 black hole), (2) a geometric phase ( AdS 2 background) and (3) a Yang–Mills phase. The Hawking process is therefore seen as an exotic line of discontinuous transitions between the gravitational and geometrical phases. Alternatively, a noncommutative nonlinear sigma model describing the transition of the dilaton field between the gravitational and geometrical phases is also constructed. [ABSTRACT FROM AUTHOR]

A consistent QM/NCG duality is put forward as a model for the AdS 2 / CFT 1 correspondence. This is a duality/correspondence between (1) the dAFF conformal quantum mechanics (QM) on the boundary (which is only "quasi-conformal" in the sense that there is neither an S O (1 , 2) -invariant vacuum state nor there are strictly speaking primary operators), and between (2) the noncommutative geometry of AdS 2 in the bulk (which is only "quasi-AdS" in the sense of being only asymptotically AdS 2 ). The Laplacian operators on noncommutative AdS 2 and commutative AdS 2 have the same spectrum and thus their correlators are conjectured to be identical. These bulk correlation functions are found to be correctly reproduced by appropriately defined boundary quantum observables in the dAFF quantum mechanics. Moreover, these quasi-primary operators on the boundary form a subalgebra of the operator algebra of noncommutative AdS 2 . [ABSTRACT FROM AUTHOR]

κ -Poincaré invariant gauge theories on κ -Minkowski space-time, which are noncommutative analogs of the usual U(1) gauge theory, exist only in five dimensions. These are built from noncommutative twisted connections on a hermitian right module over the algebra coding the κ -Minkowski space-time. We show that twisting the action of this algebra on the hermitian module, assumed to be a copy of it, affects neither the value of the above dimension nor the noncommutative gauge group defined as the unitary automorphisms of the module leaving the hermitian structure unchanged. Only the hermiticity condition obeyed by the gauge potential becomes twisted. Similarities between the present framework and algebraic features of twisted spectral triples are exhibited. [ABSTRACT FROM AUTHOR]

In this paper, the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is proposed in which noncommutative geometry can emerge from "one-matrix multitrace scalar matrix models" by probing the statistical physics of commutative phases of matter. This is in contrast to the usual mechanism in which noncommutative geometry emerges from "many-matrix singletrace Yang–Mills matrix models" by probing the statistical physics of noncommutative phases of gauge theory. In this novel scenario, quantized geometry emerges in the form of a transition between the two phase diagrams of the real quartic matrix model and the noncommutative scalar phi-four field theory. More precisely, emergence of the geometry is identified here with the emergence of the uniform-ordered phase and the corresponding commutative (Ising) and noncommutative (stripe) coexistence lines. The critical exponents and Wigner's semicircle law are used to determine the dimension and the metric, respectively. Arguments from the saddle point equation, from Monte Carlo simulation and from the matrix renormalization group equation are provided in support of this scenario. [ABSTRACT FROM AUTHOR]

In this paper, we present a quantization of the functions of spacetime, i.e. a map, analog to Weyl map, which reproduces the κ -Minkowski commutation relations, and it has the desirable properties of mapping square integrable functions into Hilbert–Schmidt operators, as well as real functions into symmetric operators. The map is based on Mellin transform on radial and time coordinates. The map also defines a deformed ∗ product which we discuss with examples. [ABSTRACT FROM AUTHOR]

Based on the gravity model as a gauge theory previously by the authors, the introduction of noncommutative structures in the very geometry is discussed and developed in a new different way. Taking into account a linear Lagrangian in curvature and considering a pair of coherent vectors responsible, among other things, for the symmetry breaking, the introduction of noncommutativity in the very structure of the geometry is achieved. The fact that the vectors are coherent states ensure not only the natural and total quantization of the model, but also the formulation of the noncommutative structure, in particular by the introduction of a star product from the convolutory properties thereof. This new star product, in a sharp contrast with other proposals, is independent of the Bargmann index or other parameters depending on the dimension of the representation of the structure group of the noncommutativity. We also explain in the same way that a matrix model, through the properties of these coherent vectors, can be easily formulated. The pros and cons of the implementation of star products versus a theory of matrices based on coset coherent states are briefly discussed. [ABSTRACT FROM AUTHOR]

Based on the presentation of the Kauffman bracket skein algebra of the thickened torus given by the third author in previous work [4], Frohman and Gelca established a complete description of the multiplicative operation leading to a famous product-to-sum formula. In this paper, we study the multiplicative structure of the Kauffman bracket skein algebra of the thickened four-holed sphere. We present an algorithm to compute the product of any two elements of the algebra, and give an explicit formula for some families of curves. We surmise that the algorithm has quasi-polynomial growth with respect to the number of crossings of a pair of curves. Further, we conjecture the existence of a positive basis for the algebra. [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]

A Gaussian approximation to the bosonic part of M-(atrix) theory with mass deformation is considered at large values of the dimension d. From the perspective of the gauge/gravity duality this action reproduces with great accuracy the stringy Hagedorn phase transition from a confinement (black string) phase to a deconfinement (black hole) phase whereas from the perspective of the matrix/geometry approach this action only captures a remnant of the geometric Yang–Mills-to-fuzzy-sphere phase where the fuzzy sphere solution is only manifested as a three-cut configuration termed the "baby fuzzy sphere" configuration. The Yang–Mills phase retains most of its characteristics with two exceptions: (i) the uniform distribution inside a solid ball suffers a crossover at very small values of the gauge coupling constant to a Wigner's semicircle law, and (ii) the uniform distribution at small values of the temperatures is nonexistent. [ABSTRACT FROM AUTHOR]

The indirect evidence for at least a dozen massive white dwarfs (WDs) violating the Chandrasekhar mass limit is considered to be one of the wonderful discoveries in astronomy for more than a decade. Researchers have already proposed a diverse amount of models to explain this astounding phenomenon. However, each of these models always carries some drawbacks. On the other hand, noncommutative geometry is one of the best replicas of quantum gravity, which is yet to be proved from observations. Madore introduced the idea of a fuzzy sphere to describe a formalism of noncommutative geometry. This paper shows that the idea of a squashed fuzzy sphere can self-consistently explain the super-Chandrasekhar limiting mass WDs. We further show that the length scale beyond which the noncommutativity is prominent is an emergent phenomenon, and there is no prerequisite for an ad hoc length scale. [ABSTRACT FROM AUTHOR]

We consider the orbits of test particles moving in the gravitational field of a noncommutative-inspired Einstein–Euler–Heisenberg black hole. Using the geometric metric, we determine the circular orbits followed by massless particles, comparing them with the circular photon orbits coming from the Plebanski pseudo-metric that takes into account the nonlinear nature of the Euler–Heisenberg electrodynamics. Using the impact parameter of the photon orbits, we define the shadow of the noncommutative-inspired black hole and discuss the constraints on the model by comparing its shadow with the prediction from General Relativity. [ABSTRACT FROM AUTHOR]

In this work, we propose a model of noncommutative cosmology through the deformation of minisuperspace. We focus on an exponentially potential with a homogeneous scalar field minimally coupled to gravity in the spatially flat universe. To process, we use a particular case of noncommutativity by making a deformation of space coordinates only. Then, we compare results in both the commutative model and the noncommutative one. [ABSTRACT FROM AUTHOR]

Chandrasekhar made the startling discovery about nine decades back that the mass of compact object white dwarf has a limiting value once nuclear fusion reactions stop therein. This is the Chandrasekhar mass-limit, which is ∼ 1. 4 M ⊙ for a nonrotating non-magnetized white dwarf. On approaching this limiting mass, a white dwarf is believed to spark off with an explosion called type Ia supernova, which is considered to be a standard candle. However, observations of several over-luminous, peculiar type Ia supernovae indicate the Chandrasekhar mass-limit to be significantly larger. By considering noncommutativity among the components of position and momentum variables, hence uncertainty in their measurements, at the quantum scales, we show that the mass of white dwarfs could be significantly super-Chandrasekhar and thereby arrive at a new mass-limit ∼ 2. 6 M ⊙ , explaining a possible origin of over-luminous peculiar type Ia supernovae. The idea of noncommutativity, apart from the Heisenberg's uncertainty principle, is there for quite sometime, without any observational proof however. Our finding offers a plausible astrophysical evidence of noncommutativity, arguing for a possible second standard candle, which has many far-reaching implications. [ABSTRACT FROM AUTHOR]

The Snyder–de Sitter model is an extension of the Snyder model to a de Sitter background. It is called triply special relativity (TSR) because it is based on three fundamental parameters: speed of light, Planck mass and cosmological constant. In this paper, we study the three-dimensional DKP oscillator for spin-0 and spin-1 in the framework of Snyder–de Sitter algebra in momentum space. By using the technique of vector spherical harmonics the energy spectrum and the corresponding eigenfunctions are obtained for the both cases. [ABSTRACT FROM AUTHOR]

In this work, we address the process of pair creation of scalar particles in (1 + 1) de Sitter space–time in presence of a constant electromagnetic field by applying the noncommutativity on the scalar field up to first-order in 𝜃. We calculate the density of particles created in the vacuum by the mean of the Bogoliubov transformations. In contrast to a previous result, we show that noncommutativity contributes to the pair creation process. We find that the noncommutativity plays the same role of chemical potential and gives an important interest for studies at high energies. [ABSTRACT FROM AUTHOR]

We review the main recent progresses in noncommutative space–time phenomenology in underground experiments. A popular model of noncommutative space–time is 𝜃 -Poincaré model, based on the Groenewold–Moyal plane algebra. This model predicts a violation of the spin-statistic theorem, in turn implying an energy and angular dependent violation of the Pauli exclusion principle. Pauli exclusion principle violating transitions in nuclear and atomic systems can be tested with very high accuracy in underground laboratory experiments such as DAMA/LIBRA and VIP(2). In this paper we derive that the 𝜃 -Poincaré model can be already ruled-out until the Planck scale, from nuclear transitions tests by DAMA/LIBRA experiment. [ABSTRACT FROM AUTHOR]

We prove a Koszul formula for the Levi-Civita connection for any pseudo-Riemannian bilinear metric on a class of centered bimodule of noncommutative one-forms. As an application to the Koszul formula, we show that our Levi-Civita connection is a bimodule connection. We construct a spectral triple on a fuzzy sphere and compute the scalar curvature for the Levi-Civita connection associated to a canonical metric. [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]

We review recent results obtained by using the spectral action applied to some simple physical models built in the noncommutative geometry framework. The first result, based on the generalization of the spectral action principle to the case of the fermionic action leads to the lowest order corrections that can possibly explain the huge difference between the electron and neutrino masses. In the second case, the extension of the family of Dirac operators for the product of finite geometry with the Riemannian manifold but without a product metric leads to a theory with two metrics that is similar to the models of bimetric gravity. [ABSTRACT FROM AUTHOR]

Using the methods of ordinary quantum mechanics, we study κ -Minkowski space as a quantum space described by noncommuting self-adjoint operators, following and enlarging T. Poulain and J.-C. Wallet, " κ -Poincaré invariant orientable field theories with at 1-loop: Scale-invariant couplings, preprint (2018), arXiv:1808.00350 [hep-th]. We see how the role of Fourier transforms is played in this case by Mellin transforms. We briefly discuss the role of transformations and observers. [ABSTRACT FROM AUTHOR]

This is a review of recent results regarding the application of Connes' noncommutative geometry to the Standard Model, and beyond. By twisting (in the sense of Connes-Moscovici) the spectral triple of the Standard Model, one does not only get an extra scalar field which stabilises the electroweak vacuum, but also an unexpected 1 -form field. By computing the fermionic action, we show how this field induces a transition from the Euclidean to the Lorentzian signature. Hints on a twisted version of the spectral action are also briefly mentioned. [ABSTRACT FROM AUTHOR]

We analyze a modified Dirac equation based on a noncommutative structure in phase space originating from a generalized uncertainty principle with a minimum length. The noncommutative structure induces generalized momenta and contributions to the energy levels of the standard Dirac equation. Applying techniques of perturbation theory, we find the lowest-order corrections to the energy levels and eigenfunctions of the Dirac equation in three dimensions for a spherically symmetric linear potential and for a square-well times triangular potential along one spatial dimension. We find that the corrections due to the noncommutative contributions may be of the same order as the relativistic ones, leading to an upper bound on the parameter fixing the minimum length induced by the generalized uncertainty principle. [ABSTRACT FROM AUTHOR]

We study covariant derivatives on a class of centered bimodules ℰ over an algebra 𝒜. We begin by identifying a 𝒵 (𝒜) -submodule 𝒳 (𝒜) which can be viewed as the analogue of vector fields in this context; 𝒳 (𝒜) is proven to be a Lie algebra. Connections on ℰ are in one-to-one correspondence with covariant derivatives on 𝒳 (𝒜). We recover the classical formulas of torsion and metric compatibility of a connection in the covariant derivative form. As a result, a Koszul formula for the Levi-Civita connection is also derived. [ABSTRACT FROM AUTHOR]

We have obtained the approximate analytical solutions of the nonrelativistic Hydrogen-like atoms such as ( He + , Li 2 + and Be +) and neutral atoms such as ( 2 2 Na , 12 C and 158 Au) atoms with a newly proposed generalized perturbed Yukawa potential with centrifugal barrier (GPYPCB) model using the generalized Bopp's shift method and standard perturbation theory in the symmetries of noncommutative three-dimensional real space phase (NC: 3D-RSP). By approximating the centrifugal term through the Greene–Aldrich approximation scheme, we have obtained the energy eigenvalues and generalized Hamiltonian operator for all orbital quantum numbers ℓ in the symmetries of NC: 3D-RSP. The potential is a superposition of the perturbed Yukawa potential and new terms proportional with (exp (− 2 a r) r 4 , exp (− 2 a r) r 3 , exp (− a r) r 3  and  exp (− a r) r 2 ) appear as a result of the effects of noncommutativity properties of space and phase on the perturbed Yukawa potential model. The obtained energy eigenvalues appear as functions of the generalized Gamma function, the discreet atomic quantum numbers (j , n , l , s  and  m) , two infinitesimal parameters (Θ , 𝜃 ¯) , which are induced by (position–position and phase–phase). In addition, the dimensional parameters (a , V 0 , V 1 , α) of perturbed Yukawa potential with centrifugal barrier model in NC: 3D-RSP. Furthermore, we have shown that the corresponding Hamiltonian operator in (NC: 3D-RSP) symmetries is the sum of the Hamiltonian operator of perturbed Yukawa potential model and the two operators are modified spin–orbit interaction and the modified Zeeman operator for the previous Hydrogenic and neutral atoms. [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 a two-parameter family of Drinfeld twists generated from a simple Jordanian twist further twisted by 1-cochains. Twists from this family interpolate between two simple Jordanian twists. Relations between them are constructed and discussed. It is proved that there exists a one-parameter family of twists identical to a simple Jordanian twist. The twisted coalgebra, star product and coordinate realizations of the κ -Minkowski noncommutative space–time are presented. Real forms of Jordanian deformations are also discussed. The method of similarity transformations is applied to the Poincaré–Weyl Hopf algebra and two types of one-parameter families of dispersion relations are constructed. Mathematically equivalent deformations, that are related to nonlinear changes of symmetry generators and linked with similarity maps, may lead to differences in the description of physical phenomena. [ABSTRACT FROM AUTHOR]

Using the gauged pseudo-Hermitian fuzzy Ginsparg–Wilson algebra, pseudo fuzzy Dirac and chirality operators on the fuzzy E A d S 2 have been studied. Also, the spectrum of the gauged pseudo fuzzy Dirac operator in the instanton sector has been studied. [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]

We examine the index data associated to twisted spectral triples and higher order spectral triples. In particular, we show that a Lipschitz regular twisted spectral triple can always be "logarithmically dampened" through functional calculus, to obtain an ordinary (i.e. untwisted) spectral triple. The same procedure turns higher order spectral triples into spectral triples. We provide examples of highly regular twisted spectral triples with nontrivial index data for which Moscovici's ansatz for a twisted local index formula is identically zero. [ABSTRACT FROM AUTHOR]

The paper builds the original foundations of a new operator theoretic setting for the study of quantum dynamics of non-perturbative aspects originated from Green's functions in Quantum Field Theory with strong couplings. [ABSTRACT FROM AUTHOR]

There ought to exist a reformulation of quantum theory which does not depend on classical time. To achieve such a reformulation, we introduce the concept of an atom of space-time-matter (STM). An STM atom is a classical noncommutative geometry (NCG), based on an asymmetric metric, and sourced by a closed string. Different such atoms interact via entanglement. The statistical thermodynamics of a large number of such atoms gives rise, at equilibrium, to a theory of quantum gravity. Far from equilibrium, where statistical fluctuations are large, the emergent theory reduces to classical general relativity. In this theory, classical black holes are far from equilibrium low entropy states, and their Hawking evaporation represents an attempt to return to the [maximum entropy] equilibrium quantum gravitational state. [ABSTRACT FROM AUTHOR]

We show that a class of braided Hopf algebras, which includes the braided S U q (2) of [P. Kasprzak, R. Meyer, S. Roy and S. L. Woronowicz, Braided quantum S U (2) groups, J. Noncommut. Geom. 10 (2016) 1161–1125], is obtained by twisting. We show further examples and demonstrate that twisting of bicovariant differential calculi gives braided bicovariant differential calculi. [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]

In this contribution, we study the effects of space noncommutativity on the Landau system for a neutral particle with induced electric dipole moment subject to a linear confining potential. We analytically solve the Schrödinger equation and obtain the complete set of energy levels and the corresponding radial wave functions for the system in terms of the noncommutativity parameter 𝜃. [ABSTRACT FROM AUTHOR]

We review the approach to the Standard Model of particle interactions based on spectral noncommutative geometry. The paper is (nearly) self-contained and presents both the mathematical and phenomenological aspects. In particular, the bosonic spectral action and the fermionic action are discussed in detail, and how they lead to phenomenology. We also discuss the Euclidean versus Lorentz issues and how to go beyond the Standard Model in this framework. [ABSTRACT FROM AUTHOR]