Faddeev-Jackiw analysis for the charged compressible fluid in a   higher-derivative electromagnetic field background
  In the present paper we will discuss the Faddeev-Jackiw symplectic approach in the analysis of a charged compressible fluid immersed in a higher-derivative electromagnetic field theory. 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. 
Albert C. R. Mendes, Everton M. C. Abreu, Jorge Ananias Neto and   Flavio I. Takakura
physics.gen-ph