Relaxation time approximation for relativistic dense matter

• Published in: Physical review. D, Particles and fields Vol. 46; no. 10; pp. 4603 - 4629
• Main Authors: HAKIM, R, MORNAS, L, PETER, P, SIVAK, H. D
• Format: Journal Article
• Language: English
• Published: Ridge, NY American Physical Society 15-11-1992
• Subjects: 662440 > Properties of Other Particles Including Hypothetical Particles > (1992-); ANGULAR MOMENTUM; CHAPMAN-ENSKOG THEORY; COUPLING CONSTANTS; CROSS SECTIONS; DISTRIBUTION FUNCTIONS; ENERGY RANGE; ENERGY-MOMENTUM TENSOR; Exact sciences and technology; FERMIONS; FIELD THEORIES; FUNCTIONS; INVARIANCE PRINCIPLES; LORENTZ INVARIANCE; MATTER; NUCLEAR MATTER; PARTICLE PROPERTIES; PERTURBATION THEORY; PHYSICAL PROPERTIES; Physics; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM CHROMODYNAMICS; QUANTUM FIELD THEORY; QUARK MATTER; QUASI PARTICLES; RELATIVISTIC RANGE; RELAXATION TIME; SPIN; Statistical physics, thermodynamics, and nonlinear dynamical systems; TENSORS; THERMAL CONDUCTIVITY; THERMODYNAMIC PROPERTIES 662230 > Quantum Chromodynamics > (1992-); TOTAL CROSS SECTIONS; Transport processes; TRANSPORT THEORY; VISCOSITY; WIGNER THEORY; Dense matter; Viscosity; Collision operator; Fermion system; Transport properties; Lorentz invariance; Relaxation time; Transport process; BGK equation; Wigner function; Spin diffusion; Kinetic equation; Thermal conductivity
• ISSN: 0556-2821; 1089-4918
• DOI: 10.1103/PhysRevD.46.4603

In this article the relaxation time approximation for a system of spin-1/2 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 {ital via} the use of covariant Wigner functions. The collision term is, of course, linear in the deviation of the Wigner function from equilibrium, and {ital 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 {ital 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) {ital 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.