Vacuum Stress Tensor of a Scalar Field in a Rectangular Waveguide

TL;DR

This paper calculates the vacuum stress tensors and local Casimir forces for a scalar field in a rectangular waveguide using heat kernel and zeta function methods, revealing local force behaviors and edge divergences.

Contribution

It introduces a detailed calculation of local vacuum stress tensors and Casimir forces in a rectangular waveguide, highlighting edge divergence issues and specific force configurations.

Findings

Explicit expressions for local stress tensors are derived.

Local Casimir forces are computed for various configurations.

Edge divergences of local forces are identified and discussed.

Abstract

Using the heat kernel method and the analytic continuation of the zeta function, we calculate the canonical and improved vacuum stress tensors, ${T_{\mu \nu}(\vec{x})}$ and ${\Theta_{\mu \nu}(\vec{x})}$, associated with a massless scalar field confined in the interior of an infinitely long rectangular waveguide. The local depence of the renormalized energy for two special configurations when the total energy is positive and negative are presented using ${T_{00}(\vec{x})}$ and ${\Theta_{00}(\vec{x})}$. From the stress tensors we obtain the local Casimir forces in all walls by introducing a particular external configuration. It is shown that this external configuration cannot give account of the edge divergences of the local forces. The local form of the forces is obtained for three special configurations.