Variations on Homological Reduction

Details Variations on Homological Reduction Variations on Homological Reduction

2007-08-25

arxiv.org/abs/0708.3598v1

Mathematics

Quantum Algebra

Ph.D. thesis, December 2006, german abstract

Scientific paper

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.

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