Symmetry transform in the Faddeev-Jackiw quantization of dual models

TL;DR

This paper explores symmetry transformations in the Faddeev-Jackiw quantization of dual models, identifying symmetry generators and completing the symplectic structure to derive Dirac brackets in specific physical theories.

Contribution

It introduces a method to identify symmetry generators within the Faddeev-Jackiw framework, enabling the complete determination of Dirac brackets in dual models.

Findings

Symmetry generators are successfully identified in the studied models.

The symplectic matrix is completed using symmetry transformations.

The approach yields the full set of Dirac brackets for the models.

Abstract

We study the presence of symmetry transformations in the Faddeev-Jackiw approach for constrained systems. Our analysis is based in the case of a particle submitted to a particular potential which depends on an arbitrary function. The method is implemented in a natural way and symmetry generators are identified. These symmetries permit us to obtain the absent elements of the sympletic matrix which complement the set of Dirac brackets of such a theory. The study developed here is applied in two different dual models. First, we discuss the case of a two-dimensional oscillator interacting with an electromagnetic potential described by a Chern-Simons term and second the Schwarz-Sen gauge theory, in order to obtain the complete set of non-null Dirac brackets and the correspondent Maxwell electromagnetic theory limit.