标题： 规范量子化超引力中的物理状态 显示英文标题

标题： Physical States in Canonically Quantized Supergravity

摘要： 我们讨论在函数Schrodinger表示中$N=1$超引力的规范量子化。尽管超对称性约束的形式表明在费米子场中有确定阶数$n$的解，但我们证明对于任何有限的$n$都没有这样的状态。对于$n=0$，一个简单的缩放论证明确排除了D'Eath所讨论的纯玻色子态。对于$n>0$，论点基于在量子化3-面上重力子场的模式展开。因此建议超引力中的物理态具有无限的Grassmann数。这对于自由自旋-3/2场得到确认，我们发现满足规范约束的态包含无限多个费米子模式算符的乘积。 显示英文摘要

摘要： 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.