New inner products for physical states in BRST quantization

Abstract

In a BRST quantization involving operators with continuous eigenvalues the naive inner products of physical states are usually undefined. In order to include such cases we propose new inner products def`ined by 〈phys|exp i[ ϱ, Q]|phys〉, where ϱ is an odd gauge-fixing operator. In this definition, which requires the use of dynamical Lagrange multipliers, the factor exp i[ ϱ, Q] is naturally provided by the choice of dynamics. Several examples are worked out. In particular it is shown that the worline supersymmetric model for a massless spin − 1 2 particle leads to fermions whose chiral projections have opposite norms.