Quantum consistency of a gauge-invariant theory of a massive spin-3/2 particle interacting with external fields

Abstract

A gauge-invariant theory of a massive spin-3/2 particle interacting with external electromagnetic and gravitational fields, obtained earlier by Kaluza-Klein reduction of a massless Rarita-Schwinger theory, is quantized using Dirac’s procedure. The field anticommutators are found to be positive definite. The theory, which was earlier shown to be free from the classical Velo-Zwanziger problem of noncausal propagation modes, is thus also free from the problem of negative-norm states, a longstanding problem associated with massive spin-3/2 theories with external interaction.