Modern approaches to the quantization of gauge theories. (English) Zbl 1040.81089

Bucker, Beatrice

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.
For the entire collection see [Zbl 1008.00022].

Reviewer: A. A. Bogush (Minsk)

MSC:

81T70	Quantization in field theory; cohomological methods
81T13	Yang-Mills and other gauge theories in quantum field theory
53D50	Geometric quantization

Keywords:

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