Boundary Conditions as Mass Generation Mechanism for Real Scalar Fields

TL;DR

This paper shows that imposing homogeneous Dirichlet boundary conditions on a massless scalar field confined between two parallel planes induces an effective mass, transforming the theory into a massive scalar field without spontaneous symmetry breaking.

Contribution

It demonstrates how boundary conditions can generate mass in scalar field theories, offering a novel mechanism for mass acquisition without symmetry breaking.

Findings

Boundary conditions induce an effective mass in the scalar field.

Spontaneous symmetry breaking does not occur under these boundary conditions.

The theory transitions from massless to massive due to boundary effects.

Abstract

We consider the effects of homogeneous Dirichlet's boundary conditions on two infinite parallel plane surfaces separated by a small distance {\it a}. We find that although spontaneous symmetry breaking does not occur for the theory of a massless, quartically self-interacting real scalar field, the theory becomes a theory of a massive scalar field.