Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time. Part 1: Klein-Gordon oscillator

TL;DR

This paper explores how non-commutativity and rotation influence a scalar field in a cosmic string space-time, revealing effects like mimicking magnetic fields and energy quantization modifications.

Contribution

It introduces a novel analysis of the Klein-Gordon oscillator considering non-commutativity and rotation, providing new insights into energy quantization and physical interpretations.

Findings

Non-commutativity mimics a magnetic field effect.

Energy quantization depends on the hard-wall boundary.

Rotation affects the confinement and energy levels.

Abstract

We analyse the Klein-Gordon oscillator in a cosmic string space-time and study the effects stemming from the rotating frame and non-commutativity in momentum space. We show that the latter mimics a constant magnetic field, imparting physical interpretation to the setup. The field equation for the scalar field is solved via separations of variables, and we obtain quantization of energy and angular momentum. The space-time metric is non-degenerate as long as the particle is confined within a hard-wall, whose position depends on the rotation frame velocity and the string mass parameter. We investigate the energy quantization both for a finite hard-wall (numerical evaluation) and in the limit of an infinite hard-wall (analytical treatment). We stress the effect of non-commutativity upon the energy quantization in each case.