Field theoretical approach to relativistic hydrodynamics

Hydrodynamics is a low-energy effective theory of a conserved charge density, which describes a long-distance and long-time behavior of many-body systems. It is applicable not only to a non-relativistic weakly-interacting dilute gas but also a relativistic strongly-interacting dense liquid like a quark-gluon plasma. The main purpose of this seminar is to explain how we can derive the hydrodynamic equation from the underlying field-theoretical description of systems [1-3]. Our derivation is based on the recent development of non-equilibrium statistical mechanics, and we show that the procedure to derive hydrodynamic equations is similar to the so-called renormalized/optimized perturbation theory. Also, to describe transport phenomena in local thermal equilibrium, we give a path-integral formula for a thermodynamic functional, which results in the emergence of thermally induced curved spacetime [2]. These results enable us to derive hydrodynamic equation based on quantum field theories.