The Casimir effect for fields with arbitrary spin

TL;DR

This paper generalizes boundary conditions for fields of arbitrary spin to analyze the Casimir effect, revealing that only two types of Casimir forces exist for massless fermionic and bosonic fields, with implications for boundary condition applications.

Contribution

It introduces universal boundary conditions for any spin field and demonstrates that the Casimir force depends solely on whether the field is fermionic or bosonic.

Findings

Allowed energy-momentum values are identical for all massless fermionic fields.

Allowed energy-momentum values are identical for all massless bosonic fields.

Periodic boundary conditions are incompatible with fermionic fields confined between plates.

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.