Dirac oscillator in dynamical noncommutative space

In this paper, we address the energy eigenvalues of two-dimensional Dirac oscillator perturbed by a dynamical noncommutative space. We derived the relativistic Hamiltonian of Dirac oscillator in the dynamical noncommutative space, in which the space-space Heisenberg-like commutation relations and noncommutative parameter are position-dependent. Then, we used this Hamiltonian to calculate the first-order correction to the eigenvalues and eigenvectors, based on the language of creation and annihilation operators 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.

Anisotropic constant-roll inflation with noncommutative model and swampland conjectures

In this paper, we study a constant-roll inflationary model in the presence of a noncommutative parameter with a homogeneous scalar field minimally coupled to gravity. The specific noncommutative inflation conditions proposed new consequences. On the other hand, we use anisotropic conditions and find new anisotropic constant-roll solutions with respect to noncommutative parameter. Also, we will plot some figures with respect to the specific values of the corresponding parameter and the swampland criteria which is raised from the exact potential obtained from the constant-roll condition. Finally, different of figures lead us to analyze the corresponding results and also show the effect of above mentioned parameter on the inflationary model.

Dirac Oscillator in Dynamical Noncommutative Space

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.

Super Ginsparg–Wilson algebra and Dirac operator on the super fuzzy Euclidean hyperboloid EAdSF(2|2)

In this paper, we construct super fuzzy Dirac and chirality operators on the super fuzzy Euclidean hyperboloid [Formula: see text] in-instanton and no-instanton sectors. Using the super pseudo-projectors of the noncompact first Hopf fibration, we construct the Ginsparg–Wilson algebra in instanton and no-instanton sectors. Then, using the generators of this algebra, we construct pseudo super-Dirac and chirality operators in both sectors. We also construct pseudo super-Dirac and chirality operators corresponding to the case in which our theory includes gauge fields. We show that they have correct commutative limit in the limit case when the noncommutative parameter [Formula: see text] tends to infinity.

q-deformed fuzzy Ginsparg–Wilson algebra and its q-deformed Dirac and chirality operators on quantum fuzzy two-sphere

We construct the [Formula: see text]-deformed fuzzy Dirac and chirality operators on quantum fuzzy Podles sphere [Formula: see text]. We will show that there are a class of these operators on [Formula: see text] in which all of them in the limit case [Formula: see text] has the correct fuzzy sphere limit as well as they have correct commutative limit in the limit case when [Formula: see text] and noncommutative parameter [Formula: see text] tends to infinity.

Fuzzy conifold YF6 and Dirac operator of principal fibration XF5 → SF2 × SF2

It has been constructed the fuzzy Dirac and chirality operators on fuzzy [Formula: see text] which is the base manifold of the principal fibration [Formula: see text]. Using the fuzzy Ginsparg–Wilson algebra, it has been studied the gauged fuzzy Dirac and chirality operators in instanton sector. It has been shown that they have correct commutative limit in the limit case when noncommutative parameter [Formula: see text] tends to infinity.

Shadow cast of noncommutative black holes in Rastall gravity

We study the shadow and energy emission rate of a spherically symmetric noncommutative black hole in Rastall gravity. Depending on the model parameters, the noncommutative black hole can reduce to the Schwarzschild black hole. Since the nonvanishing noncommutative parameter affects the formation of event horizon, the visibility of the resulting shadow depends on the noncommutative parameter in Rastall gravity. The obtained sectional shadows respect the unstable circular orbit condition, which is crucial for physical validity of the black hole image model.

Gauged Dirac operator on the quantum sphere in instanton sector

In this paper, we construct the [Formula: see text]-deformed fuzzy Dirac and chirality operators on quantum fuzzy Podles sphere [Formula: see text]. Using the [Formula: see text]-deformed fuzzy Ginsparg–Wilson algebra, we study the [Formula: see text]-deformed gauged fuzzy Dirac and chirality operators in instanton sector. We will show the correct fuzzy sphere limit in the limit case [Formula: see text] and the correct commutative limit in the limit case when [Formula: see text] and noncommutative parameter [Formula: see text] tends to infinity.

A generalized statistical complexity based on Rényi entropy of a noncommutative anisotropic oscillator in a homogeneous magnetic field

We calculate the shape Rényi and generalized Rényi complexity of a noncommutative anisotropic harmonic oscillator in a homogeneous magnetic field. To do so, we first obtain the Rényi entropy in position and momentum spaces of the exact normalized wave functions. We observe that shape Rényi and generalized Rényi complexities are monotone functions of noncommutative parameter ([Formula: see text]) in some short range in position space. We analyze the effect of the noncommutative parameter, the magnetic field and the anisotropy on shape Rényi and generalized Rényi complexities.

Dirac quasi-normal frequencies in a noncommutative black hole space–time

Noncommutative geometry may be an alternative way to quantum gravity. We study the influence of the space–time noncommutative parameter on the Dirac quasi-normal modes in the noncommutative Schwarzschild black hole space–times. In comparison to the commutative Schwarzschild black hole, the numerical results show that the oscillation frequencies and magnitude of the imaginary part of the Dirac quasi-normal modes will increase. However, it is found that the influence of the space–time noncommutative parameter on the Dirac quasi-normal modes is tiny and negligible.