Generating functions for anti-canonical transformations in the Zinn-Justin and Batalin and Vilkoviski formalisms

TL;DR

This paper explores how generating functions can be used to derive anti-canonical transformations within the BRST formalism for gauge field quantization, with applications to QCD renormalization.

Contribution

It introduces a method to obtain anti-canonical transformations from generating functions, extending classical mechanics concepts to gauge field quantization formalisms.

Findings

Derived explicit forms of anti-canonical transformations from generating functions.

Applied the method to a QCD renormalization example.

Extended the analogy between classical and quantum gauge theories.

Abstract

Quantization of gauge fields by the BRST method requires sources in addition to fields, and a bilinear anti-bracket defined in terms of them. This bracket is a sort of generalization of a Poisson bracket in classical mechanics. Canonical transformations are also generalized as anti-canonical transformations. In this paper, we take the analogy with classical mechanics one step further, by showing how anti-canonical transformations can be derived from generating functions. We give an example relevant to the renormalization of QCD in the Hamiltonian formalism.