Symplectic reduction, BRS cohomology, and infinitedimensional Clifford algebras
Abstract
This paper gives the mathematical foundations for the BRS quantization procedure. We first discuss the classical finite dimensional BRS procedure and relate it to MarsdenWeinstein reduction. This leads to interesting relations between Lie algebras and Clifford algebras and a novel way of computing Lie algebra cohomology in terms of the spin representation. We then discuss infinitedimensional Clifford algebras and their spin representations. We find that in the infinitedimensional case, the analog of the finitedimensional construction of Lie algebra cohomology breaks down, the obstruction (anomaly) being the KacPeterson class which is the cohomology class associated to the representation of the Lie algebra on spinors which is now only a projective representation. Tensoring by a projective representation of opposite class kills the obstruction and gives rise to a cohomology theory and a quantization procedure. We discuss the gradings and Hermitian structures on the absolute and relative complexes.
 Publication:

Annals of Physics
 Pub Date:
 May 1987
 DOI:
 10.1016/00034916(87)901783
 Bibcode:
 1987AnPhy.176...49K