Relaxation time approximation for relativistic dense matter.

Abstract

In this article the relaxation time approximation for a system of spin-\textonehalf{} fermions is studied with a view to calculating those transport properties obeyed by relativistic dense matter such as viscosity coefficients, thermal conductivities, spin diffusion, etc. This is achieved via the use of covariant Wigner functions. The collision term is, of course, linear in the deviation of the Wigner function from equilibrium, and a priori involves arbitrary functions of the four-momentum. These functions are restricted from physical arguments and from the requirement of Lorentz invariance. The kinetic equation obeyed by the Wigner function is then split into a mass-shell constraint and "true" kinetic equations, whose solution is sought within the Chapman-Enskog approximation. It is also realized that, in a relativistic quantum framework, there exist two expansion parameters: the new parameter occurs because of the existence of a new length scale defined by the Compton wavelength; in some cases (e.g., when the effective mass of the fermions goes to zero), this last quantity can be of the order of the mean free path. From the first-order solutions and from the Landau-Lifshitz matching conditions, the main transport properties of the system are obtained as functions of the macroscopic quantities (temperature, density, polarization) and of various relaxation times to be determined elsewhere by a specific physical model. Finally, all the results obtained are discussed and suggestions for some extensions are given.