Equivalence of Faddeev–Jackiw and Dirac Approaches for Gauge Theories

Abstract

The equivalence between the Dirac method and Faddeev–Jackiw analysis for gauge theories is proven. 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. The quantization can be achieved only in the framework of reduce and then quantize approach with all the known problems that this type of procedure presents. Finally we illustrate the equivalence by means of a particular example.