Batalin-Vilkovisky Lagrangian Quantisation

Abstract

The Lagrangian Batalin-Vilkovisky (BV) formalism gives the rules for the quantisation of a general class of gauge theories which contain all the theories known up to now. It does, however, not only give a recipe to obtain a gauge fixed action, but also gives a nice understanding of the mechanism behind gauge fixing. It moreover brings together a lot of previous knowledge and recipes in one main concept~: the canonical transformations. We explain the essentials of this formalism and give related results on the superparticle. Also anomalies (in general functions of fields and antifields) can be obtained in this formalism, and it gives the relation between anomalies in different gauges. A Pauli-Villars scheme can be used to obtain a regularised definition of the expressions at the one loop level. The calculations become similar to those of Fujikawa with the extra freedom of using arbitrary variables. A discrepancy between anomalies in light-cone gauge of the Green-Schwarz superstring and in the semi-light-cone gauge is discussed.