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Zbl 1072.81053
Bucker, Beatrice
Geometrical approaches to the quantization of gauge theories.
(English)
[A] Mladenov, Iva\"ilo 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. 111-130 (2004). ISBN 954-84952-8-7/pbk

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. [{\it M. Alexandrov, M. Kontsevich, A Schwarz} and {\it O. Zaboronsky}, Int. J. Mod. Phys. A 12, 1405-1430 (1997; Zbl 1073.81655)]. \par In this paper, these materials are utilized after a short review. Indeed, a $QP$-manifold $\prod T^*X\times\prod\frak{g} \times \frak{g}$ and the corresponding gauge invariant actions are discussed.
[Hiroshi Tamura (Kanazawa)]
MSC 2000:
*81T70 Quantization in field theory; cohomological methods
81T13 Gauge theories

Keywords: general gauge theory; BRST formalism; supermanifold; master equation

Citations: Zbl 1073.81655

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