The energy-momentum tensor,the trace identity and the Casimir effect

TL;DR

This paper investigates the violation of the trace identity related to scale transformations in electromagnetic fields with boundary conditions, highlighting differences between free space and boundary-influenced scenarios, and extending previous scalar field results.

Contribution

It demonstrates the violation of the trace identity for electromagnetic fields with boundary conditions, extending earlier work on scalar fields to the electromagnetic case.

Findings

Trace identity holds in free space but is violated at a boundary plate.

Boundary conditions affect the scale transformation properties of the electromagnetic field.

Results reinforce previous findings on scalar fields regarding boundary effects.

Abstract

The trace identity associated with the scale transformation $x^\mu\tox'{}^\mu = e^{-\rho}x^\mu$ on the Lagrangian density for the noninteracting electromagnetic field in the covariant gauge is shown to be violated on a single plate on which the Dirichlet boundary condition $A^\mu(t,x^1,x^2,x^3=-a) = 0$ is imposed.It is however respected in free space,i.e. in the absence of the plate; these results reinforce our assertions in an earlier paper where the same exercise was carried out using the Lagrangian density for the free,massive,real scalar field in 2 + 1 dimensions.