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Geometrical approaches to the quantization of gauge theories. (English) Zbl 1072.81053
Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 5th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 5–12, 2003. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-8-7/pbk). 111-130 (2004).

In BRST formalism, one needs a BRST invariant action to quantize a gauge theory. In Batalin-Vilkovisky formalism, a proper solution of classical master equation gives required action. On the other hand, it has been known that all the solutions of a classical master equation forms a $QP$-manifold – a kind of supermanifolds. [M. Alexandrov, M. Kontsevich, A Schwarz and O. Zaboronsky, Int. J. Mod. Phys. A 12, 1405-1430 (1997; Zbl 1073.81655)].

In this paper, these materials are utilized after a short review. Indeed, a $QP$-manifold $\prod {T}^{*}X×\prod 𝔤×𝔤$ and the corresponding gauge invariant actions are discussed.

##### MSC:
 81T70 Quantization in field theory; cohomological methods 81T13 Yang-Mills and other gauge theories