Generalized hydrodynamics from relativistic kinetic theory

The problem is considered of extending the Chapman-Enskog solution of the linearized transport equation for a relativistic quantum gas to the transition regime. The particular system studied is composed of various kinds of particles between which reactive processes are allowed. Following the classical approach of Ernst and Bixon, Dorfman and Mo, we construct a normal solution, as in the Chapman-Enskog procedure, but without any restriction on the wave lengths of the macroscopic disturbances. The method makes use of Zwanzig's projection-operator technique and yields a closed set of hydrodynamic equations with dissipative terms expressed as memory kernels. For small frequencies and wave vectors we recover the linearized Navier-Stokes equations with static transport coefficients given by the usual Chapman-Enskog expressions. Special attention is paid to the thermodynamic fluctuations as described by the static susceptibility matrix.     

Dynamical symmetries in relativistic kinetic theory

This paper is part of a program investigating symmetries that are defined at a physical or observational level rather than purely geometrically. Here we generalize previous work on dynamical matter symmetries of relativistic gases. If the matter symmetry vector is surface-forming with the dynamical Liouville vector, then Einstein's equations reduce it to a Killing symmetry of the metric. We show that this conclusion is unaltered if the gas particles are subject to a nongravitational force (including the electromagnetic force on charged particles) or if the gravitational field obeys higher-order field equations. In the Brans-Dicke theory, the matter symmetry reduces to a homothetic symmetry of the metric. This is also the case for a generalized conformal symmetry in Einstein's theory. We consider the problem of relaxing the surface-forming assumption in an attempt to determine whether there are dynamical symmetries that do not necessarily reduce to geometrical symmetries of the metric.     

In-medium relativistic kinetic theory and nucleon-meson systems

Within theσ —ω model of coupled nucleonmeson systems, a generalized relativistic Lennard-Balescu-equation is presented resulting from a relativistic random phase approximation (RRPA). This provides a systematic derivation of relativistic transport equations in the frame of nonequilibrium Green's function technique including medium effects as well as fluctuation effects. It contains all possible processes due to one-meson exchange and special attention is kept to the off-shell character of the particles. As a new feature of many-particle effects, processes are possible, which can be interpreted as particle creation and annihilation due to in-medium onemeson exchange. In-medium cross sections are obtained from the generalized derivation of collision integrals, which possess complete crossing symmetries.     

On relativistic kinetic gas theory: XV. The Ritz method in relativistic Boltzmann theory

The transport coefficients of a multicomponent gas mixture are approximated by means of a variational technique. It is shown that the procedure is equivalent to a more heuristic method developed earlier.     

A kinetic theory of a relativistic plasma. II

A covariant formulation of the relativistic statistical mechanics of charged particles is developed on the basis of the tetradic method, which corresponds to the super-many-time formalism of Tomonaga known in quantum theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 29–31, May, 1981.     

Induced volume forms with applications in relativistic kinetic theory

Covariant volume forms are defined in an intrinsic way on a general submanifold of aC manifold carrying a nondegenerate metric of unspecified signature. The case of covariant volume forms induced on hypersurfaces, null and nonnull, is examined in detail. The results obtained are applied to the various submanifolds of the one-particle phase space of relativistic kinetic theory. Finally a proof of Liouville's theorem is given and its consequences on the Liouville vector are discussed.     

On relativistic kinetic gas theory: XIX. The electron-neutrino system

The diffusion coefficient for a mixture of electrons and electronic neutrinos is calculated as a function of the temperature.     

General relativistic aspects of ferromagneto-fluid

The implications of Bianchi identities pertaining to the spacetime of relativistic ferrofluid with infinite conductivity and variable magnetic permeability are investigated. Some kinematical and dynamical corollaries emerging out of a preferred geometrical symmetry called an isometry with respect to the flow vector and the magnetic field vector are developed.     

Conservation laws and thermodynamic equilibrium in the general relativistic kinetic theory of inelastically interacting particles

The macroscopic conservation laws and the conditions for thermodynamic equilibrium are obtained on the basis of the general relativistic kinetic theory of inelastically interacting particles formulated by the author.     

Special relativistic gravitational theory

Based on special relativity, we introduce a way to develop a new field theory from (1) the relativistic property of the particle coupling coefficient with the field, and (2) the field due to a static point source. As an example, we discuss a theory of electromagnetic and gravitational fields. The results of this special relativistic gravitational theory for the redshift and the deflection of light are the same as those deduced from general relativity. The results of experiments on the planetary perihelion procession shift and on an additional short-range gravity are more favorable to the special relativistic gravitational theory than to general relativity. We put forward a new idea to test experimentally whether the equivalence principle of general relativity is correct.Plovdiv University Paissii Hilendarskii.Moscow Institute of Railway Transport Engineers.     

On relativistic kinetic gas theory: XVIII. Diffusion in a Lorentz gas of hard spheres

The diffusion coefficient for a relativistic Lorentz gas of hard spheres is calculated with the help of two different methods. Numerical results are given for a wide range of temperatures.     

Relativistic kinetic theory of quantum systems: I. Wigner functions for a relativistic spin-12 system

For a dilute and nondegenerate relativistic spin-$\text{1}\text{2}$ system two kinds of Wigner functions are defined: one has sixteen spinor components and the other four spin components. Their relationship is established. Statistical expressions for the current density, the energy-momentum density and the spin density are obtained in terms of both kinds of Wigner functions. The transformation properties of the latter under Lorentz transformations are discussed.     

Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory

We rederive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast with the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of motion for the dissipative currents, we directly use the latter's definition. Although the equations of motion obtained via the two approaches are formally identical, the coefficients are different. We show that, for the one-dimensional scaling expansion, our method is in better agreement with the solution obtained from the Boltzmann equation.     

On relativistic kinetic gas theory: XIV. Transport coefficients of a binary mixture. General expressions

A relativistic method to calculate transport coefficients is developed for a binary mixture with arbitrary particle interaction. The heat conductivity, the diffusion coefficient, the thermal-diffusion coefficient, the shear viscosity and the volume viscosity are expressed in terms of relativistic omega integrals.     

Landau theory of relativistic Fermi liquids

A relativistic extension of the Landau Fermi liquid theory, applicable to the study of high density matter, is developed. Consequences of Lorentz invariance in the theory are explored. The formalism is illustrated by a study of relativistic Fermi systems weakly interacting via scalar and vector meson exchange. Second order exchange energies for both massless scalar and massless vector interactions are calculated in terms of Landau parameters on the Fermi surface. Zero sound and “color-plasma oscillations” are studied in quark matter with SU(3) color gluon coupling.     

On the relativistic theory of tunneling

A relativistic generalization of the semiclassical theory of tunneling and multiphoton ionization of atoms and ions in the field of a high-intensity electromagnetic wave with linear, circular, and elliptic polarization is constructed. The exponential factor in the ionization probability is calculated for arbitrary values of adiabaticity parameter γ. In the case of low-frequency laser radiation, an asymptotically exact formula is derived for the ionization rate of the s atomic level, including the Coulomb, spin, and adiabatic corrections and the preexponential factor.     

Kinetic theory of a relativistic plasma

The BBGKY hierarchy of equations for a system of relativistic charged particles is derived. The electromagnetic field is included in the dynamical system by decomposing the transverse part of the field of each particle into oscillators. Self-consistent field equations are obtained for the relativistic plasma, and an expression is also obtained for the correlation function which leads to the Belyaev-Budker collision integral.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 78–82, March, 1981.