Rarita-Schwinger Potentials in Quantum Cosmology

TL;DR

This paper investigates the properties of Rarita-Schwinger potentials in quantum cosmology, focusing on boundary conditions, gauge transformations, and the implications for the geometry of spacetime.

Contribution

It analyzes the compatibility of boundary conditions and gauge transformations for Rarita-Schwinger potentials, and applies Penrose's secondary potentials to derive geometric restrictions.

Findings

Gauge transformations are compatible with field equations on Ricci-flat backgrounds.

Boundary conditions restrict gauge freedom.

Secondary potentials imply the background geometry must be totally flat.

Abstract

This paper studies the two-spinor form of the Rarita-Schwinger potentials subject to local boundary conditions compatible with local supersymmetry. The massless Rarita-Schwinger field equations are studied in four-real-dimensional Riemannian backgrounds with boundary. Gauge transformations on the potentials are shown to be compatible with the field equations providing the background is Ricci-flat, in agreement with previous results in the literature. However, the preservation of boundary conditions under such gauge transformations leads to a restriction of the gauge freedom. The recent construction by Penrose of secondary potentials which supplement the Rarita-Schwinger potentials is then applied. The equations for the secondary potentials, jointly with the boundary conditions, imply that the background four-geometry is further restricted to be totally flat.