Vacuum solutions for scalar fields confined in cavities

TL;DR

This paper investigates vacuum solutions for scalar fields in cavities, analyzing stability and symmetry breaking depending on cavity size and potential parameters, and introduces a general method for approximate solutions near critical lengths.

Contribution

It presents a new analysis of vacuum solutions and stability criteria for scalar fields in confined geometries, including a general method for approximate solutions near critical cavity sizes.

Findings

Zero field stability depends on cavity size and potential parameters.

Critical length exists where zero field becomes unstable.

Method for approximate solutions near critical lengths is developed.

Abstract

We look at vacuum solutions for fields confined in cavities where the boundary conditions can rule out constant field configurations, other than the zero field. If the zero field is unstable, symmetry breaking can occur to a field configuration of lower energy which is not constant. The stability of the zero field is determined by the size of the length scales which characterize the cavity and parameters that enter the scalar field potential. There can be a critical length at which an instability of the zero field sets in. In addition to looking at the rectangular and spherical cavity in detail, we describe a general method which can be used to find approximate analytical solutions when the length scales of the cavity are close to the critical value.