Relaxation time approximation for relativistic dense matter

Journal Article · Sun Nov 15 00:00:00 EST 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.46.4603· OSTI ID:7030237

Hakim, R; Mornas, L; Peter, P; Sivak, H D ^[1]

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1. Departement d'Astrophysique Relativiste et de Cosmologie, Observatoire de Meudon, 92190 Meudon (France)

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.

• OSTI ID: 7030237
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 46:10; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
NUCLEAR MATTER
TRANSPORT THEORY
QUARK MATTER
CHAPMAN-ENSKOG THEORY
COUPLING CONSTANTS
DISTRIBUTION FUNCTIONS
ENERGY-MOMENTUM TENSOR
FERMIONS
LORENTZ INVARIANCE
PERTURBATION THEORY
QUANTUM CHROMODYNAMICS
QUASI PARTICLES
RELATIVISTIC RANGE
RELAXATION TIME
SPIN
THERMAL CONDUCTIVITY
TOTAL CROSS SECTIONS
VISCOSITY
WIGNER THEORY
ANGULAR MOMENTUM
CROSS SECTIONS
ENERGY RANGE
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
MATTER
PARTICLE PROPERTIES
PHYSICAL PROPERTIES
QUANTUM FIELD THEORY
TENSORS
THERMODYNAMIC PROPERTIES
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