Geometric BRST quantization, I: Prequantization
Abstract
This is the first part of a twopart paper dedicated to the definition of BRST quantization in the framework of geometric quantization. After recognizing prequantization as a manifestation of the Poisson module structure of the sections of the prequantum line bundle, we define BRST prequantization and show that it is the homological analog of the symplectic reduction of prequantum data. We define a prequantum BRST cohomology theory and interpret it in terms of geometric objects. We then show that all Poisson structures correspond under homological reduction. This allows to prove, in the BRST context, that prequantization and reduction commute.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 February 1991
 DOI:
 10.1007/BF02100022
 Bibcode:
 1991CMaPh.136..209F