Equivalence of Faddeev-Jackiw and Dirac approaches for gauge theories

TL;DR

This paper proves the equivalence between the Dirac and Faddeev-Jackiw methods for gauge theories, showing their conceptual similarities and differences, especially regarding constraint classification and reduction procedures.

Contribution

It demonstrates the stage-by-stage equivalence of the Dirac and Faddeev-Jackiw approaches, clarifying their relationship in gauge theory analysis.

Findings

Faddeev-Jackiw and Dirac methods are equivalent for gauge theories.

F-J reduction can be viewed as a canonical transformation.

Quantization in F-J approach requires reduction before quantization.

Abstract

The equivalence between the Dirac method and Faddeev-Jackiw analysis for gauge theories is proved. In particular we trace out, in a stage by stage procedure, the standard classification of first and second class constraints of Dirac's method in the F-J approach. We also find that the Darboux transformation implied in the F-J reduction process can be viewed as a canonical transformation in Dirac approach. Unlike Dirac's method the F-J analysis is a classical reduction procedure, then the quantization can be achieved only in the framework of reduce and then quantize approach with all the know problems that this type of procedures presents. Finally we illustrate the equivalence by means of a particular example.