Non-perturbative corrections to the Casimir energy for a scalar field theory with non-linear boundary conditions

TL;DR

This paper investigates non-perturbative effects on the Casimir energy for a scalar field with non-linear boundary conditions, revealing boundary mass generation and corrections to the Casimir energy through dynamical boundary field effects.

Contribution

It introduces a novel approach to incorporate non-linear boundary conditions at the action level, demonstrating non-perturbative boundary mass generation affecting Casimir energy.

Findings

Evidence for non-perturbative 1/g^2 boundary mass generation

Correction to Casimir energy due to boundary mass effects

Dynamical boundary fields influence Casimir force calculations

Abstract

We consider the case of a free real massive bulk scalar in D=4 dimensions, and embed two parallel plates as interfaces on which we impose non-linear boundary conditions, either Dirichlet- or Neumann-like, parameterized by a new coupling constant g. This mimics a non-Abelian gauge theory supplemented with boundary conditions on surfaces embedded in the bulk. We present the first evidence for a non-perturbative 1/g^2 boundary mass generation and its ensuing correction to the standard Casimir energy. This becomes possible by incorporating dynamical corrections to the effective boundary fields, which are used to build in the boundary conditions directly at the action level.