Eur. Phys. J. C (2014) 74: 2993
https://doi.org/10.1140/epjc/s10052-014-2993-1

Regular Article - Theoretical Physics

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

¹ Department of Physics, University of Helsinki, P.O. Box 64, 00014 , Helsinki, Finland
² Instituto de Física Teórica (IFT), UNESP, São Paulo State University, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II Barra Funda, São Paulo, SP,  CEP 01140-070, Brazil

^* e-mail: rodrigo.bufalo@helsinki.fi

Received: 12 June 2014
Accepted: 21 July 2014
Published online: 7 August 2014

Abstract

In this paper we analyze two higher-derivative theories, the generalized electrodynamics and the Alekseev–Arbuzov–Baikov effective Lagrangian from the point of view of the Faddeev–Jackiw symplectic approach. It is shown that the full set of constraints is obtained directly from the zero-mode eigenvectors, and that they are in accordance with well-known results from Dirac’s theory, a recurrent issue in the literature. The method shows to be rather economical in relation to the Dirac 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.