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arXiv:2105.04644

Effects of a background scalar field induced by the Lorentz symmetry violation on Non Relativistic Quantum Mechanics

J. D. García-Aguilar

Published May 10, 2021• 0 citations
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Abstract

The extension of Standard Model of the Fundamental Particles which consider the Lorentz Symmetry Violation governed by a background tensor field presented by Colladay and Kostelecky consider the hypothesis of having a privileged direction in the space-time. Here we investigated a extension of the Schrödinger Equation inspired on that model taking into account a background scalar field. We analyze the behavior of this modified Schrödinger equation on a particle trapped in a well and quantum harmonic oscillator.

DOI
10.48550/arxiv.2105.04644

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The extension of Standard Model of the Fundamental Particles which consider the Lorentz Symmetry Violation governed by a background tensor field presented by Colladay and Kostelecky consider the hypothesis of having a privileged direction in the space-time. Here we investigated a extension of the Schrödinger Equation inspired on that model taking into account a background scalar field. We analyze the behavior of this modified Schrödinger equation on a particle trapped in a well and quantum harmonic oscillator.
Abstract We investigate the quantum dynamics of a spin-(1/2) neutral particle under the effects of Lorentz symmetry violation, characterized by a fixed time-like background vector and azimuthal electric fields added to the potential of a pure quartic oscillator. These effects, induced by the background vector that defines a preferred spacetime direction, modify the dynamics of the spin-(1/2) neutral particle and give rise to a doubly anharmonic oscillator-like potential. The main challenge is to find analytical solutions to the Schrödinger equation, considering that this nonlinear potential models realistic quantum physics scenarios. Finally, we obtain bound-state solutions in the nonrelativistic limit for the Schrödinger-Pauli equation of a spin-(1/2) neutral particle. An interesting quantum effect is observed: the constant associated with the pure quartic oscillator term is quantized, meaning it depends on the system's quantum numbers.
We analyze the nonrelativistic quantum dynamics of a single neutral spin half particle, with non-zero magnetic and electric dipole moments, moving in an external electromagnetic field in presence of Lorentz symmetry violation background. Also, we study the geometric phase for this model taking into account the parameter that breaks the Lorentz symmetry. We investigate the He-McKellar-Wilkens effect in this context and we verify that Lorentz violation parameter contribute to increase the electric dipole moment of the particle.
In this contribution, we discuss the He–McKellar–Wilkens effect and the scalar Aharonov–Bohm effect for neutral particles based on the Lorentz symmetry violation background, by showing that the background of the Lorentz symmetry violation yields Abelian quantum phases for a neutral particle. We also study the non-relativistic bound states for a neutral particle interacting with a Coulomb-like potential based on the Lorentz symmetry violation background given by a fixed vector field parallel to the radial direction.
The influence of Lorentz- and CPTCPTCPT-violating terms of the extended standard model on a semiclassical two-level system is analyzed. It is shown that the Lorentz-violating background (when coupled with the fermion sector in a vector way) is able to induce modifications on the Rabi oscillation pattern, promoting sensitive modulations on the usual oscillations. As for the term involving the coefficient coupled in an axial vector way, it brings about oscillations both on energy states and on the spin states (implied by the background). It is also seen that such backgrounds are able to yield state oscillations even in the absence of the electromagnetic field. The foreseen effects are used to establish upper bounds on the Lorentz-violating coefficients.
This article shows that one can consistently incorporate nonunitary representations of at least one group into the ``ordinary'' nonrelativistic quantum mechanics. This group turns out to be Lorentz group thus giving us an alternative approach to QFT for combining the quantum mechanics and special theory of relativity which keeps the concept of wave function (belonging to some representation of Lorentz group) through the whole theory. Scalar product has been redefined to take into the account the nonunitarity of representations of Lorentz group. Understanding parity symmetry turns out to be the key ingredient throughout the process. Instead of trying to guess an equation or a set of equations for some wave functions or fields (or equivalently trying to guess a Lagrangian for the same), one derives them based only on the superposition principle and properties of wave functions under Lorentz transformations and parity. The resulting model has striking similarities with the standard quantum field theory and yet has no negative energy states, no zitterbewegung effects, symmetric energy momentum tensor and angular momentum density tensor for \emph{all} representations of Lorentz group (unifying the theoretical description of all particles), as well as clear physical interpretation. It also offers a possible interpretation why particles and antiparticles have opposite quantum numbers.