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

Bordemann, Martin

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].

Reviewer: A.Frydryszak (Wrocław)

MSC:

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

Keywords:

deformation quantization; Fedosov method; super-Poisson bracket; symplectic supermanifolds; BRST cohomology