SUBSIDIARY CONDITIONS AND PHYSICAL S-MATRIX UNITARITY IN COVARIANT CANONICAL FORMULATION OF SUPERGRAVITY

A canonical operator formalism of supergravity in covariant gauges is presented in the framework of indefinite-metric quantum field theory. In order to specify the invariant physical subspace by a simple subsidiary condition QB|phys〉=0 with the help of the BRS charge QB, it is found necessary to adopt an unconventional form of spinor-FP-ghost Lagrangian ic ̄*∂/D {combining short solidus overlay}c slightly different from the usual one c ̄*D {combining short solidus overlay}c. By clarifying the metric structure of the total Fock space spanned by the asymptotic fields, the physical S-matrix unitarity for arbitrary gauge parameters is proved. This unitarity proof is also made simpler by the present choice of FP-ghost Lagrangian. The relationship between the present FP-ghost Lagrangian and the conventional one is also made clear. © 1979.