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. For the entire collection see [

Zbl 1008.00022].

##### MSC:

81T70 | Quantization in field theory; cohomological methods |

81T13 | Yang-Mills and other gauge theories |

53D50 | Geometric quantization |