Central potential effects induced by Lorentz symmetry violation on modified quantum oscillator field

In this paper, effects of Lorentz symmetry violation determined by a tensor field [Formula: see text] out of the Standard Model Extension on a modified quantum oscillator field in the presence of Cornell-type scalar potential are analyzed. We first introduced a scalar potential [Formula: see text] by modifying the mass square term via transformation [Formula: see text] in the Klein–Gordon equation, and then replace the momentum operator [Formula: see text], where [Formula: see text] is an arbitrary function other than [Formula: see text] to study the modified Klein–Gordon oscillator. We solve the wave equation and obtain the analytical bound-states solutions and see the dependence of oscillator frequency [Formula: see text] on the quantum numbers [Formula: see text] as well as on Lorentz-violating parameters with the potential which shows a quantum effect.

Dark Matter in the Standard Model Extension in Non-Commutative Geometry (NCG)

It is for the most part expected that dark matter is important to clarify the rotation of the galaxy, It has effectively been seen that the non-commutative geometry background can achieve this objective similarly. The objective of this study is to investigate a relationship between non-commutative geometry and certain aspect of dark matter. We are relying on a basic mathematical expression argument that indicates that the appearance of dark matter in galaxies and galaxy clusters with regard to flat rotation curves is similarly a result of non commutative geometry.

Spontaneous Lorentz Violation from Infrared Gravity

In this paper, we investigate a novel implication of the non-negligible spacetime curvature at large distances when its effects are expressed in terms of a suitably modified form of the Heisenberg uncertainty relations. Specifically, we establish a one-to-one correspondence between this modified uncertainty principle and the Standard Model Extension (SME), a string-theoretical effective field theory that accounts for both explicit and spontaneous breaking of Lorentz symmetry. This tight correspondence between string-derived effective field theory and modified quantum mechanics with extended uncertainty relations is validated by comparing the predictions concerning a deformed Hawking temperature derived from the two models. Moreover, starting from the experimental bounds on the gravity sector of the SME, we derive the most stringent constraint achieved so far on the value of the free parameter in the extended Heisenberg uncertainty principle.

Astrophysical Neutrinos in Testing Lorentz Symmetry

An overview of searches related to neutrinos of astronomical and astrophysical origin performed within the framework of the Standard-Model Extension is provided. For this effective field theory, key definitions, intriguing physical consequences, and the mathematical formalism are summarized within the neutrino sector to search for effects from a background that could lead to small deviations from Lorentz symmetry. After an introduction to the fundamental theory, examples of various experiments within the astronomical and astrophysical context are provided. Order-of-magnitude bounds of SME coefficients are shown illustratively for the tight constraints that this sector allows us to place on such violations.

The Axial Anomaly in Lorentz Violating Theories: Towards the Electromagnetic Response of Weakly Tilted Weyl Semimetals

Using the path integral formulation in Euclidean space, we extended the calculation of the abelian chiral anomalies in the case of Lorentz violating theories by considering a new fermionic correction term provided by the standard model extension, which arises in the continuous Hamiltonian of a weakly tilted Weyl semimetal, and whose cones have opposite tilting. We found that this anomaly is insensitive to the tilting parameter, retaining its well-known covariant form. This independence on the Lorentz violating parameters is consistent with other findings reported in the literature. The initially imposed gauge invariant regularization was consistently recovered at the end of the calculation by the appearance of highly non-trivial combinations of the covariant derivatives, which ultimately managed to give only terms containing the electromagnetic tensor. We emphasize that the value of the anomaly with an arbitrary parameter is not automatically related to the effective action describing the electromagnetic response of such materials.

Klein-Gordon Oscillator Under the Effects of Violation of the Lorentz Symmetry

In this work, we investigate the behaviour of relativistic quantum oscillator under the effects of Lorentz symmetry violation determined by a tensor $(K_F)_{\mu\nu\alpha\beta}$ out of the Standard Model Extension. We analyze this relativistic system under an inverse radial electric field and a constant magnetic field induced by Lorentz symmetry violation. We see that the presence of Lorentz symmetry breaking terms modified the energy spectrum of the system, and a quantum effect arise due to the dependence of the linear charge density on the quantum numbers of the system

Effects of Cornell-type Potential on Klein-Gordon Oscillator Under a Linear Central Potential Induced by Lorentz Symmetry Violation

In this work, we study a Klein-Gordon oscillator subject to Cornelltype potential in the background of the Lorentz symmetry violation determined by a tensor out of the Standard Model Extension. We introduce a Cornell-type potential S(r) = (η_L\,r + \frac{η_c}{r} ) by modifying the mass term via transformation $M → M + S(r)$ and then coupled oscillator with scalar particle by replacing the momentum operator $\vec{p}→ (\vec{p}+ i\,M\,ω\,\vec{r})$ in the relativistic wave equation. We see that the analytical solution to the Klein-Gordon oscillator equation can be achieved, and a quantum effect characterized by the dependence of the angular frequency of the oscillator on the quantum numbers of the relativistic system is observed

Relativistic Scalar Feld Under the EffEcts of Lorentz Symmetry Violation Subject to Cornell-Type Potential

We investigate a scalar particle under Lorentz symmetry breaking effects determined by a tensor out of the Standard Model Extension (SME) in the presence of a Cornell-type potential by modifying the mass term M → M +S in the KG-equation. The field configuration is such that a Coulomb-type radial electric field and a constant magnetic field can be induced by Lorentz symmetry violation, and analyze the behaviour of a scalar particle. One can see that the bound states solution to the KG-equation under the consider effects can be achieved, and a quantum effect characterized by the dependence of charge density distribution parameter on the quantum numbers of the system is observed.

Relativistic Spin-0 Particle Under Linear Central Potential Effects Induced by Lorentz Symmetry Violation

In this work, we investigate the behaviour of a relativistic scalar particle in the background of the Lorentz symmetry violation determined by a tensor (KF)µναβ out of the Standard Model Extension. A linear electric field and a uniform magnetic can be induced by the violation of the Lorentz symmetry breaking effects, and analyze the behaviour of the scalar particle. We see that the analytical solution to the KG-equation can be achieved, and a quantum effect characterized by the dependence of the magnetic field on the quantum numbers is observed