Faddeev-Jackiw analysis for the charged compressible fluid in a higher-derivative electromagnetic field background

¹ Departamento de Física, Universidade Federal de Juiz de Fora - 36036-330, Juiz de Fora - MG, Brazil
² Grupo de Física Teórica e Matemática Física, Departamento de Física, Universidade Federal Rural do Rio de Janeiro - 23890-971, Seropédica - RJ, Brazil

^(a) albert@fisica.ufjf.br
^(b) flavio@fisica.ufjf.br
^(c) evertonabreu@ufrrj.br
^(d) jorge@fisica.ufjf.br

Received: 8 June 2016
Accepted: 11 November 2016

Abstract

In the present paper we will discuss the Faddeev-Jackiw (FJ) symplectic approach in the analysis of a charged compressible fluid immersed in a higher-derivative electromagnetic field theory. In other words, we have analyzed, from the FJ point of view, the minimal coupling between the strength tensor of the fluid and the higher derivative of the electromagnetic field. We have obtained the full set of constraints directly from the zero-mode eigenvectors. Besides, we have computed the Dirac brackets for the dynamic variables of the compressible fluid. Finally, as a result of the coupling between the charged compressible fluid and the electromagnetic field we have calculated two Dirac brackets between the fluid and electromagnetic fields, which are both zero when there is no coupling between them.