Hamiltonian analysis of interacting fluids

Abstract

Ideal fluid dynamics is studied as a relativistic field theory with particular importance on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in equal-time and light-cone coordinate systems. We also consider the hamiltonian formulation of fluids interacting with an external gauge field. The complementary roles of the canonical(Noether) stress tensor and the symmetric one obtained by metric variation are discussed. Finally, a non-relativistic reduction of the system in light-cone coordinates has been carried out which reproduces results found earlier in the literature.