Applications of the Klein-Gordon equation in the Feshbach-Villars representation in the non-inertial cosmic string space-time

TL;DR

This paper investigates the relativistic quantum behavior of a spineless particle in spinning cosmic string spacetime using the Feshbach-Villars formalism applied to the Klein-Gordon equation, analyzing effects of rotation and curvature.

Contribution

It introduces the application of the Feshbach-Villars formalism to the Klein-Gordon equation in non-inertial cosmic string spacetime for various potentials, deriving energy levels and wave functions.

Findings

Rotation and curvature significantly affect energy levels.

Derived explicit wave functions for different potentials.

Analyzed the impact of non-inertial effects on quantum states.

Abstract

We study the relativistic quantum motion of a spineless particle using the Feshbach-Villars (FV) formalism in the spinning cosmic string spacetime. The movement equations are derived using the first-order FV formulation of the Klein-Gordon (KG) equation. We apply the equation of motion (a) to study the motion of the particle confined to a rigid-wall potential, (b) motion in the presence of a Coulomb-type potential, and (c) particle interacting with the Feshbach-Villars oscillator (FVO). The energy levels and wave functions are obtained for the three cases. Our study focused on the impact of rotation and curvature on the energy levels of the particle