On a relativistic scalar particle subject to a Coulomb-type potential given by Lorentz symmetry breaking effects

TL;DR

This paper explores how Lorentz symmetry breaking can induce a Coulomb-like potential affecting a relativistic scalar particle, leading to bound states and quantum effects related to confinement.

Contribution

It demonstrates that Lorentz symmetry violation can generate a Coulomb-type potential and analyzes its impact on bound states and confinement in the Klein-Gordon framework.

Findings

Lorentz symmetry breaking induces a Coulomb-like potential.

Bound states solutions are obtained for the Klein-Gordon equation.

A quantum effect links the confining potential parameter to quantum numbers.

Abstract

The behaviour of a relativistic scalar particle in a possible scenario that arises from the violation of the Lorentz symmetry is investigated. The background of the Lorentz symmetry violation is defined by a tensor field that governs the Lorentz symmetry violation out of the Standard Model Extension. Thereby, we show that a Coulomb-type potential can be induced by Lorentz symmetry breaking effects and bound states solutions to the Klein-Gordon equation can be obtained. Further, we discuss the effects of this Coulomb-type potential on the confinement of the relativistic scalar particle to a linear confining potential by showing that bound states solutions to the Klein-Gordon equation can also be achieved, and obtain a quantum effect characterized by the dependence of a parameter of the linear confining potential on the quantum numbers $\left\{n,l\right\}$ of the system.