Quantum vacuum, rotation, and nonlinear fields

TL;DR

This paper investigates the combined effects of rotation and interactions on the quantum vacuum energy, introducing new computational methods and revealing complex behaviors beyond previous simpler models.

Contribution

It extends previous Casimir energy studies to include simultaneous rotation and interactions, developing a numerical zeta function regularization approach.

Findings

Rotation and interactions jointly alter quantum vacuum energy significantly.

The coupling constant's effect is amplified by rotation, affecting energy calculations.

Deviations from massless Casimir energy behavior are observed with combined effects.

Abstract

In this paper, we extend previous results on the quantum vacuum or Casimir energy, for a noninteracting rotating system and for an interacting nonrotating system, to the case where both rotation and interactions are present. Concretely, we first reconsider the noninteracting rotating case of a scalar field theory and propose an alternative and simpler method to compute the Casimir energy based on a replica trick and the Coleman-Weinberg effective potential. We then consider the simultaneous effect of rotation and interactions, including an explicit breaking of rotational symmetry. To study this problem, we develop a numerical implementation of zeta function regularization. Our work recovers previous results as limiting cases and shows that the simultaneous inclusion of rotation and interactions produces nontrivial changes in the quantum vacuum energy. Besides expected changes (where, as the size of the ring increases for fixed interaction strength, the angular momentum grows with the angular velocity), we notice that the way rotation combines with the coupling constant amplifies the intensity of the interaction strength. Interestingly, we also observe a departure from the typical massless behavior where the Casimir energy is proportional to the inverse size of the ring.