Lorentz covariance

Quantum mechanics

Theoretical physics

Dirac equation

Relativistic wave equations

Mathematical physics

Quantum field theory

CPT symmetry

Scalar field

Classical mechanics

Physics

Nonlinear system

Coulomb

Scalar (mathematics)

Mathematics

Quantum electrodynamics

Geometry

Symmetry (geometry)

Klein–Gordon equation

Electron

Lorentz transformation

The European Physical Journal C

Inspired by the Standard Model Extension, we have investigated a possible scenario arising from the Lorentz symmetry violation governed by a background tensor field on a scalar field subject to the Klein–Gordon oscillator, where this possible scenario gives rise to a linear central potential. We analyse the behaviour of the relativistic quantum oscillator under the influence of a Coulomb-type scalar potential in this background. Then, we solve the Klein–Gordon equation analytically and discuss the influence of the background which violates the Lorentz symmetry in the relativistic energy levels.

Effects of a linear central potential induced by the Lorentz symmetry violation on the Klein–Gordon oscillator