Quantum Vacuum Fluctuations in a Chromomagnetic-like Background

TL;DR

This paper investigates quantum vacuum fluctuations of vector fields in a chromomagnetic background, analyzing Casimir energies under different boundary conditions and coupling regimes, and exploring stabilization via extra dimensions.

Contribution

It provides a detailed analysis of Casimir energies for vector fields in a chromomagnetic background, including effects of boundary conditions, polarization states, and extra dimensions.

Findings

Antiperiodic boundary conditions can alter Casimir force in weak coupling.

Introduction of a third polarization state affects Casimir energy in the background field.

Extra dimensions influence the stability of the quantum vacuum in strong coupling.

Abstract

In this paper we study the effects associated to quantum vacuum fluctuations of vectorial perturbations of the Abelian SU(2) Yang-Mills field in a static and homogeneous chromomagnetic-like background field, at zero temperature. We use periodic and antiperiodic boundary conditions in order to calculate the Casimir energy by means of the frequency sum technique and of the regularization method based on zeta functions, analyzing its behavior in the weak and strong coupling regimes. We compare the obtained results with the similar ones found for scalar and spinor fields placed in an ordinary magnetic field background. We show that only in the weak coupling regime the non-trivial topology of the system encoded in the antiperiodic boundary conditions changes the nature of the Casimir force with respect to the periodic ones. Considering the weak coupling scenario, we show that the introduction of a third polarization state in the perturbations makes manifest the effects on the Casimir energy due to the coupling with the chromomagnetic-like background field, for both the boundary conditions. Finally, in the strong coupling regime, in which the quantum vacuum is not stable due to the Nielsen-Olesen instabilities, we evaluate the effects of a compact extra dimension on its stabilization.