The Casimir effect for fields with arbitrary spin

Abstract

The Casimir force between two perfectly reflecting parallel plates is considered. In a recent paper we presented generalised physical boundary conditions describing perfectly reflecting parallel plates. These boundary conditions are applicable to a field possessing any spin, and include the well-known spin-1/2 and spin-1 boundary conditions as special cases. Here we use these general boundary conditions to show that the allowed values of energy-momentum turn out to be the same for any massless fermionic field and the same for any massless bosonic field. As a result one expects to obtain only two possible Casimir forces, one associated with fermions and the other with bosons. We explicitly verify that this is the case for the fields up to spin-2. A significant implication of our work is that periodic boundary conditions cannot be applied to a fermionic field confined between two parallel plates.