Physical States in Canonically Quantized Supergravity

Details Physical States in Canonically Quantized Supergravity Physical States in Canonically Quantized Supergravity

1994-01-28

arxiv.org/abs/hep-th/9401155v1

Nucl.Phys.B423:661-687,1994

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/0550-3213(94)90148-1

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.

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