Neumann boundary conditions inhibiting the SSB in the Coleman-Weinberg mechanism

TL;DR

This paper demonstrates that homogeneous Neumann boundary conditions can prevent the Coleman-Weinberg mechanism of spontaneous symmetry breaking in scalar electrodynamics when the spatial region is sufficiently small.

Contribution

It reveals the inhibiting effect of boundary conditions on the Coleman-Weinberg mechanism in finite regions, highlighting boundary effects on symmetry breaking.

Findings

Neumann boundary conditions inhibit the Coleman-Weinberg mechanism in small regions.

The inhibition depends on the size of the region relative to the scalar field mass.

Boundary conditions can prevent spontaneous symmetry breaking in finite systems.

Abstract

In this work we show that homogeneous Neumann boundary conditions inhibit the Coleman-Weinberg mechanism for spontaneous symmetry breaking in the scalar electrodynamics if the length of the finite region is small enough ($a = e^{2}M^{-1}_{\phi}$, where $M_{\phi}$ is the mass of the scalar field generated by the Coleman-Weinberg mechanism)