A generalized bag-like boundary condition for fields with arbitrary spin

TL;DR

This paper develops a unified boundary condition framework for massless fields of arbitrary spin, extending well-known conditions for spin-1/2 and spin-1 fields to higher spins like the graviton and gravitino.

Contribution

It introduces a generalized boundary condition applicable to any massless field of arbitrary spin, filling a gap in the treatment of higher spin boundary phenomena.

Findings

Unified boundary conditions for spin-1/2 and spin-1 fields.

Extension to higher spins including spin-2 and spin-3/2.

Potential applications to phenomena like the Casimir effect.

Abstract

Boundary conditions for the Maxwell and Dirac fields at material surfaces are widely-used and physically well-motivated, but do not appear to have been generalised to deal with higher spin fields. As a result there is no clear prescription as to which boundary conditions should be selected in order to obtain physically-relevant results pertaining to confined higher spin fields. This lack of understanding is significant given that boundary-dependent phenomena are ubiquitous across physics, a prominent example being the Casimir effect. Here, we use the two-spinor calculus formalism to present a unified treatment of boundary conditions routinely employed in the treatment of spin-1/2 and spin-1 fields. We then use this unification to obtain a boundary condition that can be applied to massless fields of any spin, including the spin-2 graviton, and its supersymmetric partner the spin-3/2 gravitino.