Derivation of covariant dissipative fluid dynamics in the renormalization-group method

We derive generic relativistic hydrodynamical equations with dissipative effects from the underlying Boltzmann equation in a mechanical and systematic way on the basis of so-called the renormalization-group method. A macroscopic frame vector is introduced to specify the frame on which the macroscopic dynamics is described. Our method is so mechanical with only few ansatz that our method gives a microscopic foundation of the available hydrodynamical equations, and also can be applied to make a reduction of the kinetic equations other than the simple Boltzmann equation.