Quantization and Renormalization and the Casimir Energy of a Scalar Field Interacting with a Rotating Ring

TL;DR

This paper analyzes the vacuum fluctuation effects on a scalar field interacting with a rotating ring, calculating the Casimir energy and angular momentum, revealing a bounded zero-point angular momentum and a non-rotating ground state.

Contribution

It introduces a collective coordinate approach to compute Casimir energy for a scalar field with a rotating background, including arbitrary interaction strength.

Findings

Zero-point angular momentum is bounded below by rac{}{24}

Ground state is generally non-rotating with positive moment of inertia

No transfer of angular momentum between zero-point and classical contributions

Abstract

Effects due to vacuum fluctuations in a semi-classical model of a massless scalar field interacting with a rotating ring are investigated by introducing a collective coordinate for the motion of the background potential. The model is solved for a repulsive periodic $\delta$-distribution background of arbitrary strength. The Casimir energy of this system is calculated in the co-rotating and, by Legendre transformation, in the stationary laboratory frame. The zero-point contribution to the angular momentum in this model is bounded below by $|\ell_{ZP}|\leq\hbar/24$ and the ground state of the entire system thus generally is non-rotating with a positive moment of inertia that decreases only slightly with increasing angular rotation frequency. There is no transfer between the zero-point and classical contributions to the total angular momentum and energy of this system at zero temperature.