Symplectic Reduction, {BRS} Cohomology, and Infinite Dimensional Clifford Algebras
Feb 3, 198795 pages
Published in:
- Annals Phys. 176 (1987) 49
Report number:
- IAS-836-87
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Abstract: (Elsevier)
This paper gives the mathematical foundations for the BRS quantization procedure. We first discuss the classical finite dimensional BRS procedure and relate it to Marsden-Weinstein 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 infinite-dimensional Clifford algebras and their spin representations. We find that in the infinite-dimensional case, the analog of the finite-dimensional construction of Lie algebra cohomology breaks down, the obstruction (anomaly) being the Kac-Peterson 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.- ALGEBRA: CLIFFORD
- ALGEBRA: LIE
- ALGEBRA: REPRESENTATION
- QUANTIZATION
- MATHEMATICAL METHODS: TOPOLOGICAL
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