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Covariant Wigner function approach to the relativistic quantum electron gas in a strong magnetic field
ANNALS
OF PHYSICS
139. 212-213
Abstracts
(1982)
of Papers to Appear
in Future
Issues
Covarianl Wigner Funcrion Approach to the Relaliristic Quantum Electron Gas in a Strong Magneric Field. R. HAKIM, Groupe d’Astrophysique Relativiste, Observatoire de Paris-Meudon, 92 190 Meudon, France. and Dkpartement de Mathimatiques, U.S.T.L.. 34060 Montpellier Cedex, France; AND H. SIVAK, Groupe d’Astrophysique Relativiste. Observatoire de Paris-Meudon. 92190 Meudon. France. This paper is concerned with a unified approach to some equilibrium properties of the relativistic quantum electron plasma embedded in a strong external magnetic field. This unified approach rests on the systematic use of a covariant Wigner function. The equilibrium Wigner function of the noninteracting gas is derived and its main properties are studied. In particular, it satisfies equations that are the complete analog of the usual Liouville equation and thus can be termed “relativistic quantum Liouville equation” whose properties are considered. The equations of state are rederived in this formalism and the results obtained earlier by Canuto and Chiu are found anew. Also, the covariant Wigner function of the magnetized vacuum is derived: it is needed, in this formalism, in order to obtain. e.g.. the vacuum polarization tensor. Since we are also interested in the plasma modes, the fluctuations of one-particle quantities-and their spectrum-(in particular, of the four current) are calculated in view of their use in the fluctuation-dissipation theorem. We also outline a microscopic proof of this theorem. on the basis of a BBGKY hierarchy for the covariant Wigner functions, and point out the existence of an effective plasma frequency.
Maximum Entropy Principle and Relatirisric H~dro~~wamics. Theoretical Physics. University of Amsterdam. Valckenierstraat Netherlands.
CH.
G.
65.
VAN
1018
Institute of Amsterdam, The
WEERT.
XE
A relativistic theory of hydrodynamics applicable beyond the hydrodynamic regime is developed on the basis of the maximum entropy principle. This allows the construction of a unique statistical operator representing the state of the system as specified by the values of the hydrodynamical densities. Special attention is paid to the thermodynamic limit and the virial theorem which leads to an expression for the pressure in terms of the field-theoretic energy-momentum tensor of Coleman and Jackiw. It is argued that outside the hydrodynamic regime the notion of a local Gibbs relation, as usually postulated, must be abandoned in general. In the context of the linear approximation, the memory-retaining and non-local generalizations of the relativistic Navier-Stokes equations are derived from the underlying Heisenberg equations of motion. The formal similarity to the Zwanzig-Mori description of non-relativistic fluids is expounded.
and
H.
FESHBACH.
of
Spin
Isospin Effects in Elastic p4He Scartering near I GeV. J. A. PARMENTOLA AND Center for Theoretical Physics. Laboratory for Nuclear Science and Department Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.
The coupled-channel method for multiple scattering is employed to describe the kJHe elasticscattering data for a proton laboratory energy of 1.03 GeV. Particular attention is paid to the double spin-flip. double isospin-flip, double spin-isospin flip and to the effects of isobar excitation of the incident proton. It is found that the presently available data are consistent with either the excitation and
212 0003-49
16/82/0302
12~2%05.00/0
Copyright All rights
‘0 1982 by Academic Press. Inc. of reproduction in any form reserved.
OF PHYSICS
139. 212-213
Abstracts
(1982)
of Papers to Appear
in Future
Issues
Covarianl Wigner Funcrion Approach to the Relaliristic Quantum Electron Gas in a Strong Magneric Field. R. HAKIM, Groupe d’Astrophysique Relativiste, Observatoire de Paris-Meudon, 92 190 Meudon, France. and Dkpartement de Mathimatiques, U.S.T.L.. 34060 Montpellier Cedex, France; AND H. SIVAK, Groupe d’Astrophysique Relativiste. Observatoire de Paris-Meudon. 92190 Meudon. France. This paper is concerned with a unified approach to some equilibrium properties of the relativistic quantum electron plasma embedded in a strong external magnetic field. This unified approach rests on the systematic use of a covariant Wigner function. The equilibrium Wigner function of the noninteracting gas is derived and its main properties are studied. In particular, it satisfies equations that are the complete analog of the usual Liouville equation and thus can be termed “relativistic quantum Liouville equation” whose properties are considered. The equations of state are rederived in this formalism and the results obtained earlier by Canuto and Chiu are found anew. Also, the covariant Wigner function of the magnetized vacuum is derived: it is needed, in this formalism, in order to obtain. e.g.. the vacuum polarization tensor. Since we are also interested in the plasma modes, the fluctuations of one-particle quantities-and their spectrum-(in particular, of the four current) are calculated in view of their use in the fluctuation-dissipation theorem. We also outline a microscopic proof of this theorem. on the basis of a BBGKY hierarchy for the covariant Wigner functions, and point out the existence of an effective plasma frequency.
Maximum Entropy Principle and Relatirisric H~dro~~wamics. Theoretical Physics. University of Amsterdam. Valckenierstraat Netherlands.
CH.
G.
65.
VAN
1018
Institute of Amsterdam, The
WEERT.
XE
A relativistic theory of hydrodynamics applicable beyond the hydrodynamic regime is developed on the basis of the maximum entropy principle. This allows the construction of a unique statistical operator representing the state of the system as specified by the values of the hydrodynamical densities. Special attention is paid to the thermodynamic limit and the virial theorem which leads to an expression for the pressure in terms of the field-theoretic energy-momentum tensor of Coleman and Jackiw. It is argued that outside the hydrodynamic regime the notion of a local Gibbs relation, as usually postulated, must be abandoned in general. In the context of the linear approximation, the memory-retaining and non-local generalizations of the relativistic Navier-Stokes equations are derived from the underlying Heisenberg equations of motion. The formal similarity to the Zwanzig-Mori description of non-relativistic fluids is expounded.
and
H.
FESHBACH.
of
Spin
Isospin Effects in Elastic p4He Scartering near I GeV. J. A. PARMENTOLA AND Center for Theoretical Physics. Laboratory for Nuclear Science and Department Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.
The coupled-channel method for multiple scattering is employed to describe the kJHe elasticscattering data for a proton laboratory energy of 1.03 GeV. Particular attention is paid to the double spin-flip. double isospin-flip, double spin-isospin flip and to the effects of isobar excitation of the incident proton. It is found that the presently available data are consistent with either the excitation and
212 0003-49
16/82/0302
12~2%05.00/0
Copyright All rights
‘0 1982 by Academic Press. Inc. of reproduction in any form reserved.