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arXiv · hep-th/9401155

Physical States in Canonically Quantized Supergravity

Sean M. Carroll·Daniel Z. Freedman·Miguel E. Ortiz·Don N. Page
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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.

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Sean M. Carroll, Daniel Z. Freedman, Miguel E. Ortiz, Don N. Page. 1994-01-28. Physical States in Canonically Quantized Supergravity. https://doi.org/10.1016/0550-3213(94)90148-1

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