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Zbl 1040.81089
Bucker, Beatrice
Modern approaches to the quantization of gauge theories. (English)
[A] Mladenov, Iva\"ilo 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. 135-152 (2003). ISBN 954-90618-4-1/pbk

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.
[A. A. Bogush (Minsk)]

MSC 2000:: *81T70 Quantization in field theory; cohomological methods
81T13 Gauge theories
53D50 Geometric quantization

Keywords: quantization of gauge theories; Lagrangian formalism; Batalin-Vilkovisky formalism; ARSZ-formalism; BRST-symmetry master equation

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