NEW INNER PRODUCTS FOR PHYSICAL STATES IN BRST QUANTIZATION

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 defined by <phys/exp i[rho, Q]/phys>, where rho is an odd gauge-fixing operator. In this definition, which requires the use of dynamical Lagrange multipliers, the factor exp i[rho, Q] is naturally provided by the choice of dynamics. Several examples are worked out. In particular it is shown that the worldline supersymmetric model for a massless spin-1/2 particle leads to fermions whose chiral projections have opposite norms.