Canonical Transformations and Gauge Fixing in the Triplectic Quantization

TL;DR

This paper explores the structure of canonical transformations and gauge fixing in triplectic quantization, revealing new constraints, solution classes, and illustrating with Yang Mills theory.

Contribution

It introduces constraints on generators of canonical transformations specific to triplectic quantization and establishes a relation between generators and gauge fixing functions.

Findings

Constraints on generators are unique to triplectic quantization.

A broad class of solutions for gauge fixing generators exists.

Application demonstrated with Yang Mills theory.

Abstract

We show that the generators of canonical transformations in the triplectic manifold must satisfy constraints that have no parallel in the usual field antifield quantization. A general form for these transformations is presented. Then we consider gauge fixing by means of canonical transformations in this Sp(2) covariant scheme, finding a relation between generators and gauge fixing functions. The existence of a wide class of solutions to this relation nicely reflects the large freedom of the gauge fixing process in the triplectic quantization. Some solutions for the generators are discussed. Our results are then illustrated by the example of Yang Mills theory.