1994/01/28 by Sean M. Carroll, Daniel Z. Freedman, Miguel E. Ortiz +1 · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #gr-qc #hep-th
paper · pdf · doi:10.1016/0550-3213(94)90148-1
published as Nucl.Phys.B423:661-687,1994 · 36 pages (uses jnl.tex), CTP #2279
arxiv created 1994/01/28 · openalex publication_date 1994/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.