Geometrical approaches to the quantization of gauge theories. (English) Zbl 1072.81053

Bucker, Beatrice

Mladenov, Ivaïlo 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 (ISBN 954-84952-8-7/pbk). 111-130 (2004).

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. [M. Alexandrov, M. Kontsevich, A Schwarz and O. Zaboronsky, Int. J. Mod. Phys. A 12, 1405–1430 (1997; Zbl 1073.81655)].
In this paper, these materials are utilized after a short review. Indeed, a \(QP\)-manifold \( \prod T^*X\times\prod\mathfrak{g} \times \mathfrak{g}\) and the corresponding gauge invariant actions are discussed.
For the entire collection see [Zbl 1048.53002].

Reviewer: Hiroshi Tamura (Kanazawa)

MSC:

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

Keywords:

general gauge theory; BRST formalism; supermanifold; master equation

Citations:

Zbl 1073.81655