Modified wave equation for spinless particles and its solutions in an external magnetic field

TL;DR

This paper develops a modified wave equation for spinless particles incorporating Lorentz violation, derives its solutions in magnetic fields, and explores quantum gravity effects on synchrotron radiation.

Contribution

It introduces a third-order derivative wave equation with Lorentz violation and provides exact solutions in magnetic fields, including quantum gravity corrections.

Findings

Modified dispersion relation derived

Exact solutions in magnetic fields obtained

Quantum gravity effects on synchrotron radiation calculated

Abstract

The wave equation for spinless particles with the Lorentz violating term is considered. We formulate the third-order in derivatives wave equation leading to the modified dispersion relation. The first-order formalism is considered and the density matrix is obtained. The Schr\"{o}dinger form of equations is presented and the quantum-mechanical Hamiltonian is found. Exact solutions of the wave equation are obtained for particles in the constant and uniform external magnetic field. The change of the synchrotron radiation radius due to quantum gravity corrections is calculated.