Local thermal behaviour of a massive scalar field near a reflecting wall

TL;DR

This paper investigates the thermal fluctuations and stress-energy behavior of a massive scalar field near reflecting walls, revealing boundary-dependent effects, a form of local dimensional reduction, and distinctions between massless and massive fields.

Contribution

It provides a detailed analysis of thermal effects near boundaries in arbitrary dimensions, highlighting boundary condition influences and the universality of local dimensional reduction.

Findings

Thermal contributions are free from boundary divergences.

The scalar field's thermal behavior differs near Dirichlet and Neumann walls.

Corrections to blackbody expressions are linear in temperature and only classical for massless fields.

Abstract

The mean square fluctuation and the expectation value of the stress-energy-momentum tensor of a neutral massive scalar field at finite temperature are determined near an infinite plane Dirichlet wall, and also near an infinite plane Neumann wall. The flat background has an arbitrary number of dimensions and the field is arbitrarily coupled to the vanishing curvature. It is shown that, unlike vacuum contributions, thermal contributions are free from boundary divergences, and that the thermal behaviour of the scalar field near a Dirichlet wall differs considerably from that near a Neumann wall. Far from the wall the study reveals a local version of dimensional reduction, namely, corrections to familiar blackbody expressions are linear in the temperature, with the corresponding coefficients given only in terms of vacuum expectation values in a background with one less dimension. It is shown that such corrections are "classical" (i.e., not dependent on Planck's constant) only if the scalar field is massless. A natural conjecture that arises is that the "local dimensional reduction" is universal since it operates for massless and massive fields alike and regardless of the boundary conditions.