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Modern approaches to the quantization of gauge theories. (English) Zbl 1040.81089
Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 4th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 6–15, 2002. Sofia: Coral Press Scientific Publishing (ISBN 954-90618-4-1/pbk). 135-152 (2003).
The problem of quantization on non-Abelian gauge field theories, taken in the “pseudo-classical” Lagrangian formulation, is considered in the framework of the known Batalin-Vilkovisky (1981, 1983, 1984) field-antifield formalism. It is taken into account that such a classical mechanical system may be described here by a solution of the classical master equation and that this solution may be treated geometrically as the so-called QP-supermanifold (related to strong homotopy Lie algebra). It is pointed out that the quantization procedure under consideration may be accomplished in closed geometrical form by using the AKSZ-formalism (1997, Alexandrov, Kontsevich, Schwarz, Zaboronsky), which reflects the BRST-symmetry (1976, Becchi, Rouet, Stora; 1976, Tyutin) of the master equation. Some questions concerning the possible extensions and applications of the presented approach to the topological quantum field theories are also briefly discussed.
MSC:
81T70Quantization in field theory; cohomological methods
81T13Yang-Mills and other gauge theories
53D50Geometric quantization