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

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 $\mathrm{\mid }{\mathrm{\ell }}_{ZP}\mathrm{\mid }\le \mathrm{\hslash }\mathrm{/}24$ 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.