Variations on Homological Reduction

Abstract

In this paper, we are concerned with the BFV-reduction of first class constraints in classsical Hamiltonian mechanics and deformation quantization. As a result, we obtain continuous star products for certain singular reduced symplectic quotients. We relate the notion of "irreducibility" of a constraint to the notion of complete intersection used in commutative algebra. We generalize the classical BFV construction to the case of projective Tate generators using a super-Poisson bracket discovered by M. Rothstein. We also discuss the problem of infinite reducibility. Several examples are elaborated on.

Ph.D. thesis, December 2006, german abstract

References in corpus (3)

• Deformation quantization of Poisson manifolds, I
• Relative formality theorem and quantisation of coisotropic submanifolds
• (Bi)modules, morphismes et réduction des star-produits: le cas symplectique, feuilletages et obstructions

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• The BRST Complex of Homological Poisson Reduction
• Invariance of the BFV-complex
• Moduli of coisotropic sections and the BFV-complex