Investigations of the torque anomaly in an annular sector. II. Global calculations, electromagnetic case

TL;DR

This paper investigates the so-called torque anomaly in electromagnetic fields within an annular sector, demonstrating that, similar to scalar cases, the anomaly can be resolved by removing linear divergences, indicating no fundamental breakdown of quantum field theory.

Contribution

The study extends previous scalar field analyses to electromagnetic fields, showing the absence of a torque anomaly when divergences are properly handled.

Findings

No torque anomaly in electromagnetic case after divergence removal

Anomaly in scalar case is linear, while electromagnetic case is nonlinear

Proper regularization removes ambiguities in torque and energy calculations

Abstract

Recently, it was suggested that there was some sort of breakdown of quantum field theory in the presence of boundaries, manifesting itself as a torque anomaly. In particular, Fulling et al. used the finite energy-momentum-stress tensor in the presence of a perfectly conducting wedge, calculated many years ago by Deutsch and Candelas, to compute the torque on one of the wedge boundaries, where the latter was cutoff by integrating the torque density down to minimum lower radius greater than zero. They observed that that torque is not equal to the negative derivative of the energy obtained by integrating the energy density down to the same minimum radius. This motivated a calculation of the torque and energy in an annular sector obtained by the intersection of the wedge with two coaxial cylinders. In a previous paper we showed that for the analogous scalar case, which also exhibited a torque anomaly in the absence of the cylindrical boundaries, the point-split regulated torque and energy indeed exhibit an anomaly, unless the point-splitting is along the axis direction. In any case, because of curvature divergences, no unambiguous finite part can be extracted. However, that ambiguity is linear in the wedge angle; if the condition is imposed that the linear term be removed, the resulting torque and energy is finite, and exhibits no anomaly. In this paper, we demonstrate the same phenomenon takes place for the electromagnetic field, so there is no torque anomaly present here either. This is a nontrivial generalization, since the anomaly found by Fulling et al. is linear for the Dirichlet scalar case, but nonlinear for the conducting electromagnetic case.