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

Abstract

The trace identity associated with the scale transformation $x^μ\tox'{}^μ= e^{-ρ}x^μ$ 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 $A^μ(t,x^1,x^2,x^3=-a) = 0$ 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.