Faddeev-Jackiw Quantization of the Gauge Invariant Self-dual Fields Relative to String Theory

TL;DR

This paper applies the Faddeev-Jackiw symplectic method to quantize gauge invariant self-dual fields interacting with gauge fields, demonstrating its simplicity and equivalence to Dirac's method in this context.

Contribution

It introduces a new symplectic Lagrangian density and compares FJ and Dirac quantization methods, highlighting FJ's efficiency and simplicity.

Findings

FJ and Dirac methods yield equivalent quantization results.

FJ method simplifies the quantization process by avoiding classification of constraints.

FJ method is more economical and effective for gauge invariant self-dual fields.

Abstract

We obtain a new symplectic Lagrangian density and deduce Faddeev-Jackiw (FJ) generalized brackets of the gauge invariant self-dual fields interacting with gauge fields. We further give FJ quantization of this system. Furthermore, the FJ method is compared with Dirac method, the results show the two methods are equivalent in the quantization of this system. And by the practical research in this letter, it can be found that the FJ method is really simpler than the Dirac method, namely, the FJ method obviates the need to distinguish primary and secondary constraints and first- and second-class constraints. Therefore, the FJ method is a more economical and effective method of quantization.