BRST COHOMOLOGY AND HILBERT-SPACES OF NON-ABELIAN MODELS IN THE DECOUPLED PATH-INTEGRAL FORMULATION

The existence of several nilpotent Noether charges in the decoupled fo rmulation of two-dimensional gauge theories does not imply that all of these are required to annihilate the physical states. We elucidate th is matter in the context of simple quantum mechanical and field theore tical models, where the structure of the Hilbert space is known. We pr ovide a systematic procedure for deciding which of the BRST conditions is to be imposed on the physical states in order to ensure the equiva lence of the decoupled formulation to the original, coupled one. (C) 1 997 Academic Press.