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In this paper, we address the energy eigenvalues of two-dimensional Dirac oscillator perturbed by dynamical noncommutative space. We derived the relativistic Hamiltonian of Dirac oscillator in dynamical noncommutative space ( τ -space), in which the space-space Heisenberg–like commutation relations and noncommutative parameter are position-dependent. Then used this Hamiltonian to calculate the first-order correction to the eigenvalues and eigenvectors, based on the second quantization and using the perturbation theory. It is shown that the energy shift depends on the dynamical noncommutative parameter τ . Knowing that with a set of two-dimensional Bopp-shift transformation, we mapped the noncommutative problem to the standard commutative one.

The aim of this manuscript is to discuss the wormhole geometry in f ( R ) theory of gravity, where R represents the Ricci scalar. For our current work, we consider the spherically symmetric static spacetime with an anisotropic fluid source to discuss the wormhole solutions. We further discuss the existence of wormholes by using two well-known distributions like Gaussian and Lorentzian non-commutative geometry. The stability of wormhole geometry has been discussed through the Tolman–Oppenheimer–Volkoff equation and observed that our wormhole solutions are stable. Furthermore, we analyse the anisotropic parameter to examine the behaviour of the wormhole. It can be observed through the graphical analysis that null energy conditions (NEC) are not satisfied for these distributions. The violation of NEC indicates the existence of dark matter and dark energy, which is the validation of Gaussian and Lorentzian non-commutative wormholes exist in the modified f ( R ) theory of gravity.

Assume that the function $f:[0,\infty )\rightarrow \mathbb {R}$ is operator monotone in $[0,\infty )$ . We can define the perspective $\mathcal {P}_{f}\left (B,A\right ) $ by setting $$ \mathcal{P}_{f}\left( B,A\right) :=A^{1/2}f\left( A^{-1/2}BA^{-1/2}\right) A^{1/2}, $$ where A, B > 0. In this paper, we show among others that, if σ ≥ C ≥ ρ > 0, D > 0, ς ≥ Q ≥ τ > 0 and 0 < n ≤ D − C ≤ N for some constants ρ, σ, ς, τ, n, N, then $$ \begin{array}{@{}rcl@{}} 0& \le& \frac{n}{N{\varsigma}^{2}}\left[ \mathcal{P}_{f}\left( {\varsigma} ,N+\sigma \right) -\mathcal{P}_{f}\left( {\varsigma} ,\sigma \right) \right] Q^{2} \\ & \leq& \mathcal{P}_{f}\left( Q,D\right) -\mathcal{P}_{f}\left( Q,C\right) \\ & \leq& \frac{N}{n\tau^{2}}\left[ \mathcal{P}_{f}\left( \tau ,n+\rho \right) -\mathcal{P}_{f}\left( \tau ,\rho \right) \right] Q^{2}. \end{array} $$ Applications for the weighted operator geometric mean and the perspective $$ \mathcal{P}_{\ln \left( \cdot +1\right) }\left( B,A\right) :=A^{1/2}\ln \left( A^{-1/2}BA^{-1/2}+1\right) A^{1/2},~ A,B>0 $$ are also provided.

Let E be a separable symmetric space on 0 , ∞ and E M the corresponding noncommutative space. In this paper, we introduce a kind of quasimartingale spaces which is like but bigger than E M and obtain the following interpolation result: let E ^ M be the space of all bounded E M -quasimartingales and 1 < p < p E < q E < q < ∞ . Then, there exists a symmetric space F on 0 , ∞ with nontrivial Boyd indices such that E ^ M = L ^ p M , L ^ q M F , K .

Gravitational well is a widely used system for the verification of the quantum weak equivalence principle (WEP). We have studied the quantum gravitational well (GW) under the shed of noncommutative (NC) space so that the results can be utilized for testing the validity of WEP in NC-space. To keep our study widely usable, we have considered both position-position and momentum-momentum noncommutativity. Since coherent state (CS) structure provides a natural bridging between the classical and quantum domain descriptions, the quantum domain validity of purely classical phenomena like free-fall under gravity might be verified with the help of CS. We have constructed CS with the aid of a Lewis-Riesenfeld phase space invariant operator. From the uncertainty relations deduced from the expectation values of the observables, we have shown that the solutions of the time-dependent Schr\"{o}dinger equation are squeezed-coherent states., Comment: arXiv admin note: substantial text overlap with arXiv:2006.11252

Noncommutative phase space of arbitrary dimension is discussed. We introduce momentum-momentum noncommutativity in addition to co-ordinate-coordinate noncommutativity. We find an exact form for the linear transformation which relates a noncommutative phase space to the corresponding ordinary one. By using this form, we show that a noncommutative phase space of arbitrary dimension can be represented by the direct sum of two-dimensional noncommutative ones. In two-dimension, we obtain the transformation which relates a noncommutative phase space to commutative one. The transformation has the Lorentz transformation-like forms and can also describe the Bopp's shift.

A connection between the deformed Duffin–Kemmer–Petiau (DKP) algebra and an extended system of the parafermion trilinear commutation relations for the creation and annihilation operators $$a^{\pm }_{k}$$ a k ± and for an additional operator $$a_{0}$$ a 0 obeying para-Fermi statistics of order 2 based on the Lie algebra $${\mathfrak {s}}{\mathfrak {o}}(2M+2)$$ s o ( 2 M + 2 ) is established. An appropriate system of the parafermion coherent states as functions of para-Grassmann numbers is introduced. The representation for the operator $$a_{0}$$ a 0 in terms of generators of the orthogonal group SO(2M) correctly reproducing action of this operator on the state vectors of Fock space is obtained. A connection of the Geyer operator $$a_{0}^{2}$$ a 0 2 with the operator of so-called G-parity and with the CPT- operator $${\hat{\eta }}_{5}$$ η ^ 5 of the DKP-theory is established. In a para-Grassmann algebra a noncommutative, associative star product $$*$$ ∗ (the Moyal product) as a direct generalization of the star product in the algebra of Grassmann numbers is introduced. Two independent approaches to the calculation of the Moyal product $$*$$ ∗ are considered. It is shown that in calculating the matrix elements in the basis of parafermion coherent states of various operator expressions it should be taken into account constantly that we work in the so-called Ohnuki and Kamefuchi’s generalized state-vector space $${\mathfrak {U}}_{\;G}$$ U G , whose state vectors include para-Grassmann numbers $$\xi _{k}$$ ξ k in their definition, instead of the standard state-vector space $${\mathfrak {U}}$$ U (the Fock space).

This study describes the Rastall modified theory with noncommutative Gaussian- and Lorentzian-like distributions to find spherical and symmetric wormhole solutions. The basic concept of noncommutative geometry with both distributions is a physically acceptable and significant topic of quantum physics. It becomes more illustrious and interesting when we combine it with the concept of wormhole geometry. Therefore, it calculates the viable and physically realistic solutions for wormhole existential geometry under Gaussian and Lorentzian frameworks. Further, in the presence of Gaussian and Lorentzian distributions, the feasible and acceptable wormhole solutions are shown graphically. Furthermore, the stability analysis is discussed by using the Tolman–Oppenheimer–Volkov equation for all of the solutions under Gaussian- and Lorentzian-like distributions in the Rastall framework. For this purpose, we will take suitable particular values of the free and dimensionless parameters. At the end, it is concluded that our obtained solutions are physically arguable.

We present a general procedure for constructing exact black hole (BH) solutions with the magnetic charge in the context of nonlinear electrodynamics (NED) theory as well as in the coherent state approach to noncommutative geometry (NCG). In this framework, the Lagrangian density for the noncommutative Hayward BH is obtained and the weak energy condition (WEC) is satisfied. The noncommutative Hayward solution depends on two kind of charges which for the vanishing of them yields the Schwarzschild solution. Moreover, in order to find a link between the BH evaporation and uncertainty relations, we may calculate the Hawking temperature and find the effect of the Lagrangian density of BHs on the Hawking radiation. Therefore, a generalized uncertainty principle (GUP) emerges from the modified Hawking temperature in Einstein-NED theory. The origin of this GUP is the combined influence of a nonlinear magnetic source and an intrinsic property of the manifold associated with a fictitious charge. Finally, we find that there is an upper bound on the Lagrangian uncertainty of the BHs which are sourced by the NED field and/or the fictitious charge., 24 pages, 3 figures, 1 table, new issues in Introduction and new References are added, Title is changed, minor revisions in Abstract and Conclusions

The differential cross-section of the top quark pair production via the quark-antiquark annihilation subprocess in hadron collision is calculated within the noncommutative standard model. A pure NC analytical expression for the forward-backward asymmetry at the tree level is obtained. Moreover, using recent Tevatron results from the full RUN2 data, a new lower bound on the noncommutative geometry parameter is deduced.

Understanding nonequilibrium transport is crucial for controlling energy flow in nanoscale systems. We study thermal energy transfer in a generalized nonequilibrium spin-boson model (NESB) with noncommutative system-bath coupling operators and discover its unusual transport properties. Compared to the conventional NESB, the energy current is greatly enhanced by rotating the system-bath coupling operators. Constructive contribution to thermal rectification can be optimized when two sources of asymmetry, system-bath coupling strength and coupling operators, coexist. At the weak coupling and the adiabatic limit, the scaling dependence of energy current on the coupling strength and the system energy gap changes drastically when the coupling operators become noncommutative. These scaling relations can further be explained analytically by the nonequilibrium polaron-transformed Redfield equation (NE-PTRE). These novel transport properties, arising from the pure quantum effect of noncommutative coupling operators, suggest an unvisited dimension of controlling transport in nanoscale systems and should generally appear in other nonequilibrium set-ups and driven systems.

A generalization of the noncommutative reduction of the relativistic wave equations in external electromagnetic fields admitting functional arbitrariness is proposed. Electromagnetic fields with functional arbitrariness, admitting noncommutative integration of the relativistic Klein–Gordon wave equation with respect to symmetry algebras containing the operator P0 + P3 are constructed.

We show that it is in principle possible to construct dualities between commutative and non-commutative theories in a systematic way. This construction exploits a generalization of the exact renormalization group equation (ERG). We apply this to the simple case of the Landau problem and then generalize it to the free and interacting non-canonical scalar field theory. This constructive approach offers the advantage of tracking the implementation of the Lorentz symmetry in the non-commutative dual theory. In principle, it allows for the construction of completely consistent non-commutative and non-local theories where the Lorentz symmetry and unitarity are still respected, but may be implemented in a highly non-trivial and non-local manner.

In this paper, decoherence of a damped anisotropic harmonic oscillator in the presence of a magnetic field is studied in the framework of the Lindblad theory of open quantum systems in noncommutative phase-space. General fundamental conditions that should follow our quantum mechanical diffusion coefficients appearing in the master equation are kindly derived. From the master equation, the expressions of density operator, the Wigner distribution function, the expectation and variance with respect to coordinates and momenta are obtained. Based on these quantities, the total energy of the system is evaluated and simulations show its dependency to phase-space structure and its improvement due to noncommutativity effects and the environmental temperature as well. In addition, we also evaluate the decoherence time scale and show that it increases with noncommutativity phase-space effects as compared to the commutative case. It turns out from simulations that this time scale is significantly improved under magnetic field effects.

By a diagonal embedding of $U(1)$ in $SU_q(m)$, we prolongate the diagonal circle action on the Vaksman-Soibelman quantum sphere $S^{2n+1}_q$ to the $SU_q(m)$-action on the prolongated bundle. Then we prove that the noncommutative vector bundles associated via the fundamental representation of $SU_q(m)$, for $m\in\{2,\ldots,n\}$, yield generators of the even K-theory group of the C*-algebra of the Vaksman-Soibelman quantum complex projective space $\mathbb{C}{\rm P}^n_q$., 8 pages

Virtual black holes in noncommutative spacetime are investigated using coordinate coherent state formalism such that the event horizon of black hole is manipulated by smearing it with a Gaussian of width $ \sqrt \theta $, where $ \theta$ is the noncommutativity parameter. Proton lifetime, the main associated phenomenology of the noncommutative virtual black holes, has been studied: first in $4$ dimensional spacetime and then generalized to $D$ dimensions. The lifetime depends on $ \theta$ and the number of spacetime dimensions such that it emphasizes on the measurement of proton lifetime as a potential probe for the micro-structure of spacetime., Comment: 8 pages, 4 figures

We study the topic of quantum differentiability on quantum Euclidean $d$-dimensional spaces (otherwise known as Moyal $d$-spaces), and we find conditions that are necessary and sufficient for the singular values of the quantised differential to have decay $O(n^{-\alpha})$ for $0 < \alpha \leq \frac{1}{d}$. This result is substantially more difficult than the analogous problems for Euclidean space and for quantum $d$-tori., Comment: Accepted to Comm. Math. Phys

We develop an approach to the study of Coulomb branch operators in 3D $\mathcal{N}=4$ gauge theories and the associated quantization structure of their Coulomb branches. This structure is encoded in a one-dimensional TQFT subsector of the full 3D theory, which we describe by combining several techniques and ideas. The answer takes the form of an associative and noncommutative star product algebra on the Coulomb branch. For `good' and `ugly' theories (according to the Gaiotto-Witten classification), we also exhibit a trace map on this algebra, which allows for the computation of correlation functions and, in particular, guarantees that the star product satisfies a truncation condition. This work extends previous work on abelian theories to the non-abelian case by quantifying the monopole bubbling that describes screening of GNO boundary conditions. In our approach, monopole bubbling is determined from the algebraic consistency of the OPE. This also yields a physical proof of the Bullimore-Dimofte-Gaiotto abelianization description of the Coulomb branch., Comment: 73 pages plus appendices; v2: improved presentation, updated references and acknowledgements, added comments and appendices; v3: fixed a reference, matches published version

In this study, the deformed Klein–Gordon equation, Dirac equation, and Schrödinger equations were solved with the improved the modified Mobius square potential model (IMSPM, in short) using Bopp’s shift and standard perturbation theory methods in the symmetries of extended quantum mechanics. By employing the improved approximation to the centrifugal term, the relativistic and nonrelativistic bound state energies were obtained for some selected diatomic molecules (H2, I2, CO, NO, and HCl). The relativistic shift energy ΔEmsptot(n,α,A,B,V0,Θ,σ,χ,j,l,s,m) and the perturbative nonrelativistic corrections ΔEmspnr(n,α,A,B,V0,Θ,σ,χ,j,l,s,m) appeared as a function of the parameters (α,A,B,V0), the parameters of noncommutativity (Θ,σ,χ), in addition to the atomic quantum numbers (n,j,l,s,m). In both relativistic and nonrelativistic problems, we show that the corrections on the spectrum energy are smaller than the main energy in the ordinary cases of RQM and NRQM. A straightforward limit of our results to ordinary quantum mechanics shows that the present result under the improved modified Mobius square potential model is consistent with what is obtained in the literature. In the new symmetries of NCQM, is not possible to get the exact analytical solutions for l=0 and l≠0 can only be solved approximately. Through this research, we came to two noteworthy results, the first is related to the deformed Klein-Gordon equation under the influence of the improved modified Mobius square potential model becomes equivalent to the Duffin-Kemmer equation for a meson with spin-s, while the second result concerns the deformed Schrödinger equation, which can now describe the state of high-energy fermionic particles similar to the Dirac equation in the literature.

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.

In the present article we review the work carried out by us and collaborators on supersymmetric quantum cosmology, noncommutative quantum cosmology and the application of GUPs to quantum cosmology and black holes. The review represents our personal view on these subjects and it is presented in chronological order.

In this paper, within the framework of relativistic quantum mechanics and using the improved approximation scheme to the centrifugal term for any [Formula: see text]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 [Formula: see text]. 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 [Formula: see text] and [Formula: see text] of the (scalar vector) Hellmann potential, the screening range parameter [Formula: see text], the dissociation energy of the vector, and scalar potential [Formula: see text], the equilibrium inter-nuclear distance [Formula: see text] in addition to the atomic quantum numbers [Formula: see text]. 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.

The relativistic Lorentz-covariant quantum space-times obtained by Snyder can be described by the coset generators of (anti) de-Sitter algebras. Similarly, the Lorentz-covariant quantum phase spaces introduced by Yang, which contain additionally quantum curved fourmomenta and quantum-deformed relativistic Heisenberg algebra, can be defined by suitably chosen coset generators of conformal algebras. We extend such algebraic construction to the respective superalgebras, which provide quantum Lorentz-covariant superspaces (SUSY Snyder model) and indicate also how to obtain the quantum relativistic phase superspaces (SUSY Yang model). In last Section we recall briefly other ways of deriving quantum phase (super)spaces and we compare the spinorial Snyder type models defining bosonic or fermionic quantum-deformed spinors., 15 pages, LaTeX

Usually, the realizations of the noncommutative Snyder model lead to a nonassociative star product. However, it has been shown that this problem can be avoided by adding to the spacetime coordinates new tensorial degrees of freedom. The model so obtained, called extended Snyder model, can be subject to a $\kappa$-deformation, giving rise to a unification of the Snyder and the $\kappa$-Poincar\'e algebras in the formalism of extended spacetime. In this paper we review this construction and consider the generic realizations of the $\kappa$-deformed extended Snyder model, calculating the associated star product, coproduct and twist in a perturbative setting. We also introduce a representation of the Lorentz algebra in the extended space and speculate on possible interpretations of the tensorial degrees of freedom., Comment: 11 pages; version accepted for publication on Phys. Rev. D

We build the bosonic η-deformed AdS4 × $$ \mathbbm{CP} $$ CP 3 background generated by an r-matrix that satisfies the modified classical Yang-Baxter equation. In a special limit we find that it is the gravity dual of the noncommutative ABJM theory.

In this study, the analytical solutions of the Klein–Gordon equation for any [Formula: see text] states of the modified effective mass potential under the modified unequal scalar and vector Coulomb–Hulthén potential (MUSVCH-P) are derived by using an approximation method to the centrifugal potential term in the symmetries of relativistic noncommutative three-dimensional real space (RNC: 3D-RS). The new analytical expressions for eigenvalues of the energy spectrum and the new mass of mesons, such as charmonium and bottomonium that have the quark and antiquark flavor, have been estimated by using Bopp’s shift method, and perturbation theory. The energy state equation depends on the global parameters characterizing the noncommutativity space and the potential parameter [Formula: see text] in addition to the Gamma function and the discreet atomic quantum numbers [Formula: see text]. The expression for the new energy spectra is applied to obtain the new mass spectra of heavy quarkonium systems (charmonium and bottomonium) in the symmetries of (RNC: 3D-RS). The comparisons show that our theoretical results are in very good agreement with the reported works.

The indirect evidence for at least a dozen massive white dwarfs 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 article shows that the idea of a squashed fuzzy sphere can self-consistently explain the super-Chandrasekhar limiting mass white dwarfs. 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., 20 pages including 7 figures; text is modified and references are updated: Accepted for publication in IJMPD

Integrals of motion are constructed from noncommutative (NC ) Kepler dynamics, generating $$\mathrm{SO}(3)$$ , $$\mathrm{SO}(4)$$ , and $$\mathrm{SO}(1,3)$$ dynamical symmetry groups. The Hamiltonian vector field is derived in action–angle coordinates, and the existence of a hierarchy of bi-Hamiltonian structures is highlighted. Then, a family of Nijenhuis recursion operators is computed and discussed.

We consider the possibility of having Dark Matter (DM) black holes motivated by the Einasto density profile. This generalizes both the noncommutative mini black hole model and allows DM to enter as the matter constituent which makes up the black hole. We show that it is possible to construct a black hole solution for each value of the Einasto index and for different values of the mass parameter, provided that the we work with the energy-momentum tensor of an anisotropic fluid. In particular, we achieve that by first considering the equation of state (EOS) $p_r=-\rho$. It turns out that the corresponding black hole solution exhibits a horizon structure similar to that of a Reissner-Nordstr\"{o}m black hole and the central singularity is replaced by a regular de Sitter core. We also show that if the previous EOS is replaced by a nonlocal one, it is possible to construct a self-gravitating fuzzy DM droplet but also in this case, the radial pressure is negative. Finally, we contemplate scenarios of different dark matter black holes with moderate mass values which could have formed in galaxies. In particular, we probe the possibility whether such black holes could also be the central galactic objects., Comment: 20 pages, 15 figures

Continuing the study of the Moyal Higher Spin Yang–Mills theory started in our previous paper we provide a detailed discussion of matter coupling and the corresponding tree-level amplitudes. We also start the investigation of the spectrum by expanding the master fields in terms of ordinary spacetime fields. We note that the spectrum can be consistent with unitarity while still preserving Lorentz covariance, albeit not in the usual way, but by employing an infinite-dimensional unitary representation of the Lorentz group.

The complete classification of classical $r$-matrices generating quantum deformations of the (3+1)-dimensional (A)dS and Poincar\'e groups such that their Lorentz sector is a quantum subgroup is presented. It is found that there exists three classes of such $r$-matrices, one of them being a novel two-parametric one. The (A)dS and Minkowskian Poisson homogeneous spaces corresponding to these three deformations are explicitly constructed in both local and ambient coordinates. Their quantization is performed, thus giving rise to the associated noncommutative spacetimes, that in the Minkowski case are naturally expressed in terms of quantum null-plane coordinates, and they are always defined by homogeneous quadratic algebras. Finally, non-relativistic and ultra-relativistic limits giving rise to novel Newtonian and Carrollian noncommutative spacetimes are also presented., Comment: 30 pages; v2 matches version accepted by Class. Quant. Grav. Comments and references added. The (2+1)-dimensional case is described in new section 4.1

In this research work, within the framework of relativistic and nonrelativistic noncommutative quantum mechanics, the deformed Klein–Gordon and Schrödinger equations were solved with the modified equal vector scalar Manning-Rosen potential that has been of significance interest in recent years using Bopp's shift method and standard perturbation theory in the first-order in the noncommutativity parameters in 3-dimensions noncommutative quantum mechanics. By employing the improved approximation of the centrifugal term, the relativistic and nonrelativistic bound state energies were obtained for some diatomic molecules such as (HCl, CH, LiH, CO, NO, O2, I2, N2, H2, and Ar2). The obtained energy eigenvalues appear as a function of the generalized Gamma function, the parameters of noncommutativity, and the parameters of studied potential, in addition to the atomic quantum numbers . In both relativistic and nonrelativistic problems, we show that the corrections on the spectrum energy are smaller than the main energy in the ordinary cases of RQM and NRQM. A straightforward limit of our results to ordinary quantum mechanics shows that the present result is consistent with what is obtained in the literature. We have seen that the improved approximation of the centrifugal term is better than the other approximations in finding the approximate analytical solutions of the Klein-Gordon and Schrödinger equations for the modified Manning–Rosen potential in RNCQM and NRNCQM.

Fragmentation is known as the dominant production mechanism of hadrons with large transverse momentum and forms the nonperturbative and little known aspect of hadroproduction process. In the present work, we calculate the fragmentation function of gluon into pseudoscalar heavy quarkonia to the leading order in $$\alpha _s$$ in the standard model as well as the noncommutative QCD framework. To study the noncommutative effects, we apply the Seiberg–Witten maps to the first order of the noncommutative parameter $$\theta ^{\mu \nu }$$ . Our study shows that for the large values of gluon transverse momentum, the noncommutative effects show up for $$\Lambda _{\mathrm{NC}}

We study symmetry properties and the possibility of exact integration of the time-independent Schrödinger equation in an external electromagnetic field. We present an algorithm for constructing the first-order symmetry algebra and describe its structure in terms of Lie algebra central extensions. Based on the well-known classification of the subalgebras of the algebra e(3), we classify all electromagnetic fields for which the corresponding time-independent Schrödinger equations admit first-order symmetry algebras. Moreover, we select the integrable cases, and for physically interesting electromagnetic fields, we reduced the original Schrödinger equation to an ordinary differential equation using the noncommutative integration method developed by Shapovalov and Shirokov.

Motivated by the strong constraints to noncommutative quantum theories coming from Gamma Ray Bursts and the precision attained by SQUID devices in measuring magnetic fields, we study in this article the thermodynamic behaviour of a Fermi gas subject to the action of a background magnetic field, in two and three dimensional space with noncommutative coordinates and momenta. An explicit expression is obtained for the magnetization and magnetic susceptibility of the gas, both for Landau’s diamagnetism and Pauli’s paramagnetism. We are lead in this way to an upper bound $$\theta \lesssim (10 \,\text {Gev})^{-2}$$ for the noncommutative parameter.

Quantum aspects of a moving neutral particle possessing a magnetic quadrupole moment that interacts with an axial electric field in the presence of a two-dimensional harmonic oscillator are investigated in the background of noncommutative space. The energy levels of bound states and the corresponding wave functions are obtained using analytical method. It is shown that the effects of space noncommutativity and harmonic oscillator modify the spectrum of energy and remove the degeneracy of the Landau-type system. Furthermore, solutions of bound states as well as the associated wave functions are also investigated in the context of noncommutative space when the magnetic quadrupole moment interacts with a radial magnetic field under the two-dimensional harmonic oscillator using the Frobenius method. As quantum effect, it is shown that the harmonic oscillator frequency becomes determined by the quantum numbers of the system and by the noncommutativity parameter $$\theta $$ . In order to show the effects of space noncommutativity on the system, some figures are also presented.

We construct and study a simple noncommutative scheme (theta-deformation) for the effective loop quantum cosmology of the flat Friedmann-Lema\^{\i}tre-Robertson-Walker model in the presence of a homogeneous scalar field $\ensuremath{\phi}$ with a potential $\mathcal{V}(\ensuremath{\phi})=\frac{1}{2}{m}^{2}{\ensuremath{\phi}}^{2}$. We first conduct a simple analysis from the corresponding Hamilton equations of motion considering a generic term $\mathcal{V}(\ensuremath{\phi})$. It is observed that the characteristic big bounce of loop quantum cosmology is preserved under such noncommutative extension. When specializing to the quadratic case, numerical solutions to the corresponding Hamilton equations exhibiting an early inflationary epoch with a sufficiently large number of $e$-foldings are found. It is concluded that, in this noncommutative setup, solutions exist which are in the overall compatible with the early universe predicted by standard (effective) Loop Quantum Cosmology (i.e., a bouncing and inflationary early universe). The issue of the genericness of a sufficiently long inflationary period on the space of solutions in this noncommutative construct remains to be addressed.

We have studied the charged BTZ black holes in noncommutative spaces arising from two independent approaches. First, by using the Seiberg-Witten map followed by a dynamic choice of gauge in the Chern-Simons gauge theory. Second, by inducing the fuzziness in the mass and charge by a Lorentzian distribution function with the width being the same as the minimal length of the associated noncommutativity. In the first approach, we have found the existence of non-static and non-stationary BTZ black holes in noncommutative spaces for the first time in the literature, while the second approach facilitates us to introduce a proper bound on the noncommutative parameter so that the corresponding black hole becomes stable and physical. We have used a contemporary tunneling formalism to study the thermodynamics of the black holes arising from both of the approaches and analyze their behavior within the context., Comment: 16 pages, 5 figures

A model for an expanding noncommutative acoustic fluid analogous to a Friedmann-Robertson-Walker geometry is derived. For this purpose, a noncommutative Abelian Higgs model is considered in a (3+1)-dimensional spacetime. In this scenario, we analyze the motion of test particles in this fluid. The study considers a scalar test particle coupled to a quantized fluctuating massless scalar field. For all cases studied, we find corrections due to the noncommutativity in the mean squared velocity of the particles. The nonzero velocity dispersion for particles that are free to move on geodesics disagrees with the null result found previously in the literature for expanding commutative fluid., Comment: 16 pages, 4 figures, version accepted in PRD

It is known that Noncommutative QED (NCQED) exhibits Gribov ambiguities in the Landau gauge. These ambiguities are related to zero modes of the Faddeev-Popov operator and arise in the ghost propagator when it has a pole. In this work, we establish a positive Faddeev-Popov operator for NCQED and the condition for the ghost propagator not to have poles, the so-called Gribov no-pole condition. This condition is implemented in the path integral, and allows for the calculation of the photon propagator in momentum space, which is dependent on the squared non-commutativity parameter. In the commutative limit standard QED is recovered., 20 pages

The Snyder-de Sitter (SdS) model which is invariant under the action of the de Sitter group, is an example of a noncommutative spacetime with three fundamental scales. In this paper, we considered the massless Dirac fermions in graphene layer in a curved Snyder spacetime which are subjected to an external magnetic field. We employed representation in the momentum space to derive the energy eigenvalues and the eigenfunctions of the system. Then, we used the deduced energy function obtaining the internal energy, heat capacity, and entropy functions. We investigated the role of the fundamental scales on these thermal quantities of the graphene layer. We found that the effect of the SdS model on the thermodynamic properties is significant., 11 pages, 4 figures

We propose a general procedure to construct noncommutative deformations of an embedded submanifold M of $${\mathbb {R}}^n$$ R n determined by a set of smooth equations $$f^a(x)=0$$ f a ( x ) = 0 . We use the framework of Drinfel’d twist deformation of differential geometry of Aschieri et al. (Class Quantum Gravity 23:1883, 2006); the commutative pointwise product is replaced by a (generally noncommutative) $$\star $$ ⋆ -product determined by a Drinfel’d twist. The twists we employ are based on the Lie algebra $$\Xi _t$$ Ξ t of vector fields that are tangent to all the submanifolds that are level sets of the $$f^a$$ f a (tangent infinitesimal diffeomorphisms); the twisted Cartan calculus is automatically equivariant under twisted $$\Xi _t$$ Ξ t . We can consistently project a connection from the twisted $${\mathbb {R}}^n$$ R n to the twisted M if the twist is based on a suitable Lie subalgebra $${\mathfrak {e}}\subset \Xi _t$$ e ⊂ Ξ t . If we endow $${\mathbb {R}}^n$$ R n with a metric, then twisting and projecting to the normal and tangent vector fields commute, and we can project the Levi–Civita connection consistently to the twisted M, provided the twist is based on the Lie subalgebra $${\mathfrak {k}}\subset {\mathfrak {e}}$$ k ⊂ e of the Killing vector fields of the metric; a twisted Gauss theorem follows, in particular. Twisted algebraic manifolds can be characterized in terms of generators and $$\star $$ ⋆ -polynomial relations. We present in some detail twisted cylinders embedded in twisted Euclidean $${\mathbb {R}}^3$$ R 3 and twisted hyperboloids embedded in twisted Minkowski $${\mathbb {R}}^3$$ R 3 [these are twisted (anti-)de Sitter spaces $$dS_2,AdS_2$$ d S 2 , A d S 2 ].