Physical States in Canonically Quantized Supergravity

Abstract

We discuss the canonical quantization of $N=1$ supergravity in the functional Schrodinger 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.

36 pages (uses jnl.tex), CTP #2279

References in corpus (4)

• Supersymmetric Bianchi class A models
• Canonical Quantum Supergravity in Three Dimensions, (some lines lost during submission)
• Physical States in d=3,N=2 Supergravity
• Physical states in $N=1$ supergravity

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