Boundary Terms for Massless Fermionic Fields

TL;DR

This paper investigates boundary conditions and boundary terms for massless fermionic fields in classical and quantum cosmology, revealing links with spectral boundary conditions and deriving the boundary term in the action functional.

Contribution

It provides a detailed analysis of classical boundary-value problems and boundary terms for massless fermionic fields, connecting supersymmetry-induced conditions with spectral boundary conditions.

Findings

Boundary conditions involve Euclidean normal and independent spinor fields.

A link is established between classical boundary-value problems and spectral boundary conditions.

The boundary term in the action functional is explicitly derived.

Abstract

Local supersymmetry leads to boundary conditions for fermionic fields in one-loop quantum cosmology involving the Euclidean normal to the boundary and a pair of independent spinor fields. This paper studies the corresponding classical properties, i.e. the classical boundary-value problem and boundary terms in the variational problem. Interestingly, a link is found with the classical boundary-value problem when spectral boundary conditions are imposed on a 3-sphere in the massless case. Moreover, the boundary term in the action functional is derived.