Causality Versus Gauge Invariance in Quantum Gravity and Supergravity

Abstract

It is proposed that one should admit in the path integral for the quantized gravitational field only those space-times for which the final three-geometry is located in the future of the initial one. As a consequence, and unlike the situation for the Yang-Mills field, the resulting causal amplitude is not annihilated by all the gauge (surface deformation) generators. In supergravity the causal amplitude turns out not to be annihilated by the local supersymmetry generators either.