Geometrical interpretation of the functional measure for supersymmetric gauge theories and of the gauge invariant effective action
The standard quantization method for field theories involves functional path integration over fields. The formalism makes use of superspace, in which each point is a field over ordinary space. Since the fields themselves may commute or anti-commute, the resulting space is described by coordinates some of which commute and others anti-commute. Such a space is referred to as ``supersymmetric.'' Furthermore, the fields in question, Yang-Mills, are subject to transformations (gauge) which must leave the underlying physics unchanged and thus must leave invariant physically significant quantities. As a result, the functional integral must be done in an invariant way. This paper is concerned with describing in a geometrical way techniques for dealing with this problem. This involves first defining a metric on superspace leading to a gauge invariant measure. Next the gauge invariance of the Lagrangian itself must be assured, in particular when treated perturbatively. An invariant approach to this is then provided by the introduction of an invariant connection, leading to expansions involving covariant derivatives. This paper provides a brief overview of many aspects of these problems, together with some applications and bibliography.
scientific article; zbMATH DE number 4213081
scientific article