Matching high and low temperature regimes of massive scalar fields

TL;DR

This paper studies how high and low temperature expansions of the effective action for massive scalar fields between walls relate, revealing exponential decay of vacuum energy and boundary condition effects.

Contribution

It provides a detailed analysis of the matching between high and low temperature regimes for scalar fields with different boundary conditions.

Findings

Vacuum energy decays exponentially with wall separation at low temperatures.

Decay rate is halved for boundary conditions linking the two walls.

Dirichlet boundary conditions have twice the decay rate of periodic conditions.

Abstract

We analyze the matching of high and low temperature expansions of the effective action of massive scalar fields confined between two infinite walls with different boundary conditions. One remarkable low temperature effect is the exponential decay of the vacuum energy with the separation of the walls and the fact that the rate of decay is half for the boundary conditions which involve a connection between the boundary conditions of the two walls. In particular, the rate for Dirichlet boundary conditions is double than that of periodic boundary conditions.