The deformation quantization of certain super-Poisson brackets and BRST cohomology. (English) Zbl 1004.53067

Dito, Giuseppe (ed.) et al., Conférence Moshé Flato 1999: Quantization, deformations, and symmetries, Dijon, France, September 5-8, 1999. Volume II. Dordrecht: Kluwer Academic Publishers. Math. Phys. Stud. 22, 45-68 (2000).
The author gives an account of the generalization of the Fedosov method of deformation quantization to the case of super-Poisson bracket. He discusses a construction of the quantized BRST-cohomology for locally free Hamiltonian Lie group actions, and moreover, a construction of the classical BRST-cohomology in reducible first-class case without using the “ghost for ghost” scheme. The work systematizes and improves some of previously obtained results.
For the entire collection see [Zbl 0949.00040].


53D55 Deformation quantization, star products
81T70 Quantization in field theory; cohomological methods
58C50 Analysis on supermanifolds or graded manifolds
81Q60 Supersymmetry and quantum mechanics
81S99 General quantum mechanics and problems of quantization
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