Generalized Classical BRST Cohomology and Reduction of Poisson Manifolds

Details Generalized Classical BRST Cohomology and Reduction of Poisson Manifolds Generalized Classical BRST Cohomology and Reduction of Poisson Manifolds

1992-07-23

arxiv.org/abs/hep-th/9207080v1

Commun.Math.Phys. 151 (1993) 155-182

Physics

High Energy Physics

High Energy Physics - Theory

33

Scientific paper

10.1007/BF02096751

In this paper, we formulate a generalization of the classical BRST construction which applies to the case of the reduction of a poisson manifold by a submanifold. In the case of symplectic reduction, our procedure generalizes the usual classical BRST construction which only applies to symplectic reduction of a symplectic manifold by a coisotropic submanifold, \ie\ the case of reducible ``first class'' constraints. In particular, our procedure yields a method to deal with ``second-class'' constraints. We construct the BRST complex and compute its cohomology. BRST cohomology vanishes for negative dimension and is isomorphic as a poisson algebra to the algebra of smooth functions on the reduced poisson manifold in zero dimension. We then show that in the general case of reduction of poisson manifolds, BRST cohomology cannot be identified with the cohomology of vertical differential forms.

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