QCD gauge symmetries through Faddeev-Jackiw symplectic method

TL;DR

This paper applies the Faddeev-Jackiw symplectic method to analyze Yang-Mills theories, demonstrating how starting from U(1) electromagnetism can lead to constructing non-Abelian gauge theories like SU(3).

Contribution

It introduces a novel approach to deriving non-Abelian gauge symmetries from Abelian theories using the Faddeev-Jackiw formalism.

Findings

Successfully constructed SU(3)-like gauge theories from U(1) electromagnetism.

Provided insights into the structure of Yang-Mills theories via symplectic analysis.

Enhanced understanding of gauge symmetry emergence in constrained systems.

Abstract

The interactions between gluons are important in theories such as quantum chromodynamics. Therefore, to rediscover new features of well known methods in order to investigate the SU(3) gauge group can be a new way to deal with Yang-Mills theories. In this work we analyzed YM theories through the well known Faddeev-Jackiw formalism for constrained systems. Besides, we showed precisely that having U(1) Maxwell electromagnetic theory as a starting point we can construct SU(3)-like and SU(3) X SU(2) X U(1) non-Abelian theories.