Remi HAKIM

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I am a former professor (now retired) in Theoretical Physics at Paris University. I am presently interested by Middle East people.

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Exterior Differential Forms

Collective Oscillations of a Relativistic Radiating Electron Plasma

The Physics of fluids, Dec 1, 1971

Results obtained previously are applied to the study of the dispersion relations of a relativisti... more Results obtained previously are applied to the study of the dispersion relations of a relativistic radiating electron gas. The cases of (a) supraluminous and (b) suprathermal waves are dealt with. It is found that the effect of radiation is a negligibly small damping except for longitudinal supraluminous modes which are strongly damped. The stream instability is also studied, and it is shown that the more relativistic a beam is, the more unstable it is.

Statistical bootstrap in wonderland (comments on an amusing cosmological model)

NASA STI/Recon Technical Report N, Jun 1, 1975

Curved Space–Time and Cosmology

WORLD SCIENTIFIC eBooks, Mar 1, 2011

Physical Constants

Gravitation and Special Relativity

Cambridge University Press eBooks, May 20, 1999

A mathematical derivation of Maxwell's equations for gravitation, based on a mathematical proof o... more A mathematical derivation of Maxwell's equations for gravitation, based on a mathematical proof of Faraday's Law, is presented. The theory provides a linear, relativistic Lagrangian field theory of gravity in a weak field, and paves the way to a better understanding of the structure of the energy-momentum tensor in the Einstein Field Equations. Hence it is directly relevant to problems in modern cosmology. The derivation, independent of the perturbation theory of Einstein's equations, puts the gravitational and electromagnetic fields on an equal footing for weak fields, contrary to generally held views. The historical objections to a linear Lorentz invariant field theory of gravity are refuted.

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Strong Magnetic Fields

Relativistic Stochastic Processes and Related Questions

The One-Particle Relativistic Distribution Function

Applications of relativistic kinetic theory to cosmological models: some observational consequences

Astronomy and Astrophysics, Jun 1, 1973

A gas, consisting of clusters of galaxies, was studied using kinetic theory. It was assumed to ha... more A gas, consisting of clusters of galaxies, was studied using kinetic theory. It was assumed to have been in equilibrium at some arbitrarily earlier epoch, and to have ihe density observed at the present time. The model was also assigned a finite pressure. An equation of state was abstracted together with a number of observables: these were used to establish a comparison with other Friedmann models. The actual computations were prformed for the magnitude redshift diagram with a particular velocity distribution, and a comparison with observation lead to the conclusion that when clusters of galaxies are treated as test particles, their random velocities do not exceed some value close to 4500 km/ s. The significance of this result, and also some other applications of the same model, are discussed. (auth)

The inflationary universe : A primer

Springer eBooks, Oct 29, 2005

... For instance, whether the Universe started with a sym-metry between matter and antimatter, or... more

Remarks on Relativistic Statistical Mechanics. II. Hierarchies for the Reduced Densities

Journal of Mathematical Physics, Jul 1, 1967

In Paper I the basis of relativistic statistical mechanics was discussed and notions such as phas... more In Paper I the basis of relativistic statistical mechanics was discussed and notions such as phase space, Gibbs ensemble, distribution functions were defined. Paper II deals with hierarchies of equations for the reduced densities. Extensive use is made of the beautiful methods of Klimontovich. In this way ``classical mesic interactions'' are dealt with neglecting ``radiation'' effects (i.e., ``classical'' emission of mesons). It is shown how the ``renormalization of mass'' affects the hierarchies obtained. Electromagnetic interactions are dealt with: (a) neglecting radiation effects, (b) including radiation effects. The latter case is treated on the basis of the Lorentz-Dirac equations and with the help of suitable modifications of the formalism. In this way a new approach to radiation phenomena (for instance, in plasmas) is obtained. Finally, as a matter of illustration, several well-known relativistic kinetic equations are rederived in a slightly improved manner (i.e., Vlasov and Landau equations).

Sur la mécanique statistique relativiste

Annales De L Institut Henri Poincare-physique Theorique, 1967

Annales de l'I. H. P., section A, tome 6, n o 3 (1967), p. 225-244 <http © Gauthier-Villars, 1967... more Annales de l'I. H. P., section A, tome 6, n o 3 (1967), p. 225-244 <http © Gauthier-Villars, 1967, tous droits réservés. L'accès aux archives de la revue « Annales de l'I. H. P., section A » implique l'accord avec les conditions générales d'utilisation (). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques

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A Covariant Theory of Relativistic Brownian Motion I. Local Equilibrium

Journal of Mathematical Physics, Oct 1, 1965

The Vlasov Equations of a Relativistic Plasma

Compt. Rend., Apr 1, 1965

Remarks on the Quark-Hadron Transition in the Early Universe

A first-order phase-transition model of the quark-hadron transition of the early universe is inve... more A first-order phase-transition model of the quark-hadron transition of the early universe is investigated theoretically. The dynamics of the quark-gluon system are characterized; the quark plasma is described statistically; and the effects of fluctuations in various basic parameters are evaluated. It is shown that uncertainties in such areas as quark-quark potential, quark mass, and three-body correlations lead to a wide

Statistical mechanics of relativistic dense matter

La Rivista Del Nuovo Cimento, Jun 1, 1978

A general formalism is given for the statistical description of strongly interacting particles fo... more A general formalism is given for the statistical description of strongly interacting particles forming relativistic dense matter. This formalism, which is based on the use of covariant Wigner distributions, is illustrated by an application to a simple model consisting of spin 1/2 baryons interacting with a scalar meson field via a Yukawa-like coupling. Previous works on dense matter are reviewed,

Relativistic Kinetic Equations Including Radiation Effects. I. Vlasov Approximation

Journal of Mathematical Physics, 1968

In a preceding series of papers, we developed relativistic statistical mechanics of electromagnet... more In a preceding series of papers, we developed relativistic statistical mechanics of electromagnetically interacting particles. Here we derive a hierarchy of manifestly covariant equations for the reduced densities. This hierarchy is valid at order one in a parameter which is closely related to radiation phenomena. At the lowest order (absence of correlation between particles), we derive a kinetic equation which is a modification of the relativistic Vlasov equation. The added term introduces the effects of the emission of collective radiation. A dimensional analysis shows that this term is important when mc2 ∼ kT, i.e., when the plasma is relativistic. The modified Vlasov equation is shown to be irreversible: an H theorem is proved. Several applications are studied: dispersion relations, hydrodynamical equations. We have also discussed the Einstein-Ritz controversy on the connection between retarded actions and irreversibility.

Remarks on Relativistic Statistical Mechanics. I

Journal of Mathematical Physics, Jun 1, 1967

The modifications introduced by the specific forms of relativistic dynamics of many-particle syst... more The modifications introduced by the specific forms of relativistic dynamics of many-particle systems are shown to give rise to a different (with respect to the nonrelativistic case) manner to set the problems involved in a tentative construction of relativistic statistical mechanics. Although the difficult problems of relativistic dynamics are not solved, it is possible to define relativistic generalizations of phase space, distribution functions, Gibbs ensembles, and average values. In particular, phase space is chosen for convenience and is no longer related (as is usually the case) to the ``initial data,'' whose nature is yet unknown. As a consequence, only those observables which depend on the variables characterizing phase space give rise to easily computed average values. However, it is possible to enlarge at will the basic phase space and to define subsequent densities from which average values may be calculated. [Example: The calculation of average values of observables A(…xiμ,uiμ…) needs only densities of the form N(…xiμ,uiμ…) and observables involving acceleration variables need the enlarging of phase space so as to include the latter. On this enlarged phase space, densities of the form N(…xiμ,uiμ,γiμ…) may be defined and are used to compute average values, etc.] The notion of equilibrium is discussed and suggestions for reaching the solution of this unsolved problem are made.

Application to Nuclear Matter

WORLD SCIENTIFIC eBooks, Mar 1, 2011

Remi HAKIM

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