Casimir effect for a perfectly conducting wedge in terms of local zeta function

TL;DR

This paper calculates the electromagnetic vacuum energy density inside a conducting wedge using local zeta function regularization, simplifying the process and deriving finite, physically meaningful results relevant to cosmic string backgrounds.

Contribution

It introduces a local zeta function approach to compute vacuum energy in a wedge, avoiding divergences and simplifying calculations with Hertz potentials.

Findings

Finite expression for energy density obtained without subtractions

High temperature behavior of Casimir quantities scales as T^2

Results applicable to scalar fields and cosmic string backgrounds

Abstract

The vacuum energy density of electromagnetic field inside a perfectly conducting wedge is calculated by making use of the local zeta function technique. This regularization completely eliminates divergent expressions in the course of calculations and gives rise to a finite expression for the energy density in question without any subtractions. Employment of the Hertz potentials for constructing the general solution to the Maxwell equations results in a considerable simplification of the calculations. Transition to the global zeta function is carried out by introducing a cutoff nearby the cusp at the origin. Proceeding from this the heat kernel coefficients are calculated and the high temperature asymptotics of the Helmholtz free energy and of the torque of the Casimir forces are found. The wedge singularity gives rise to a specific high temperature behaviour $\sim T^2$ of the quantities under consideration. The obtained results are directly applicable to the free energy of a scalar massless field and electromagnetic field on the background of a cosmic string.