Casimir Effect in Problems with Spherical Symmetry: New Perspectives

Since Maxwell’s theory is a gauge theory, it is quite important to evaluate the corresponding zero-point energy by a careful assignment of boundary conditions on the potential and on the ghost fields. Recent work by the authors has shown that, for a perfectly conducting spherical shell, it is precisely the contribution of longitudinal and normal modes of the potential which enables one to reproduce the result first due to Boyer. For arbitrary values of a gauge parameter, however, the difficult problem remains of having to solve an entangled system of three eigenvalue equations. Such a problem is crucial both for the foundations and for the applications of quantum field theory.