Physical states in canonically quantized supergravity

Abstract

We discuss the canonical quantization of N=1 supergravity in the functional Schrödinger representation. Although the form of the supersymmetry constraints suggests that there are solutions of definite order n in the fermion fields, we show that there are no such states for any finite n. For n=0, a simple scaling argument definitively excludes the purely bosonic states discussed by D'Eath. For n>0, the argument is based on a mode expansion of the gravitino field on the quantization 3-surface. It is thus suggested that physical states in supergravity have infinite Grassmann number. This is confirmed for the free spin-3/2 field, for which we find that states satisfying the gauge constraints contain an infinite product of fermion mode operators.