Quantum equation of motion for a particle in the field of primordial fluctuations

TL;DR

This paper derives a quantum equation of motion for a particle in a brane universe, incorporating topology variations, and provides solutions and dispersion relations within this framework.

Contribution

It introduces a novel quantum equation of motion for particles in a brane universe considering topology changes, advancing theoretical understanding.

Findings

Derived the equation of motion including topology variation terms

Obtained approximate solutions for the particle's behavior

Derived dispersion relations for particles in the brane context

Abstract

Brane model of universe is considered for a particle. Conservation laws inside the brane are obtained. Equation of motion is derived for a particle using variation principle from these conservation laws. This equation includes terms accounting the variation of brane topology. Its solution is obtained at some approximations and dispersion relation for a particle is derived.