Hydrodynamic approach to many-body systems: exact conservation laws

In this paper I present a pedagogical derivation of continuity equations manifesting exact conservation laws in an interacting electronic system based on the nonequilibrium Keldysh technique. The purpose of this exercise is to lay the groundwork for extending the hydrodynamic approach to electronic transport to strongly correlated systems where the quasiparticle approximation and Boltzmann kinetic theory fail.