Faddeev-Jackiw quantization of four dimensional BF theory

TL;DR

This paper applies the Faddeev-Jackiw symplectic method to analyze four-dimensional BF theory, demonstrating its efficiency and equivalence to Dirac's formalism in deriving constraints and brackets.

Contribution

It provides a detailed symplectic analysis of 4D BF theory using Faddeev-Jackiw approach, highlighting its advantages over Dirac's method.

Findings

Faddeev-Jackiw constraints match Dirac's constraints

Generalized Faddeev-Jackiw brackets coincide with Dirac brackets

Faddeev-Jackiw method is more economical than Dirac's formalism

Abstract

The symplectic analysis of a four dimensional $BF$ theory in the context of the Faddeev-Jackiw symplectic approach is performed. It is shown that this method is more economical than Dirac's formalism. In particular, the complete set of Faddeev-Jackiw constraints and the generalized Faddeev-Jackiw brackets are reported. In addition, we show that the generalized Faddeev-Jackiw brackets and the Dirac ones coincide to each other. Finally, the similarities and advantages between Faddeev-Jackiw method and Dirac's formalism are briefly discussed.