Higher-derivative non-Abelian gauge fields via the Faddeev-Jackiw formalism

TL;DR

This paper applies the Faddeev-Jackiw formalism to analyze higher-derivative non-Abelian gauge theories, demonstrating an efficient way to identify constraints and constructing the transition amplitude using a BRST approach.

Contribution

It introduces a streamlined method for deriving constraints in higher-derivative gauge theories and extends the analysis to non-Abelian cases with a BRST-based transition amplitude.

Findings

Constraints obtained directly from zero-mode eigenvectors

Method aligns with Dirac's results but is more economical

Constructed the transition amplitude for the non-Abelian theory

Abstract

In this paper we analyze two higher-derivative theories, the generalized electrodynamics and the Alekseev-Arbuzov-Baikov's effective Lagrangian from the point of view of Faddeev-Jackiw sympletic approach. It is shown that the full set of constraint is obtained directly from the zero-mode eigenvectors, and that they are in accordance with known results from Dirac's theory, a remnant and recurrent issue in the literature. The method shows to be rather economical in relation to the Dirac's one, obviating thus unnecessary classification and calculations. Afterwards, to conclude we construct the transition-amplitude of the non-Abelian theory following a constrained BRST-method.