Lorentz symmetry of subdynamics in relativistic systems

Ben-Ya'acov, Uri

doi:10.1016/0378-4371(95)00285-5

Cited by 7 publications

(23 citation statements)

References 11 publications

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“…Our results can be extended to relativity where the Poincaré group splits into two semigroups. 26,27 The main entity is probability, and the time symmetry is broken. Nature evolves as a semigroup.…”

Section: From Being To Becomingmentioning

confidence: 99%

Laws of Nature and Time Symmetry Breaking

Antoniou

1999

Annals of the New York Academy of Sciences

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Section: From Being To Becomingmentioning

confidence: 99%

Laws of Nature and Time Symmetry Breaking

Antoniou

1999

Annals of the New York Academy of Sciences

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“…Such picture is encapsulated in Eqs. (17) and (19), which constitute a manifestly covariant version of the Bogoliubov functional assumption-the general principle underlying kinetic processes of manybody systems.…”

Section: Discussionmentioning

confidence: 99%

“…The remaining of this paper is, indeed, devoted to the applications of Eqs. (17)- (19) in classical relativistic plasmas with electromagnetic interactions.…”

Section: B General Transport Equation and Hierarchy Of Physical Corrmentioning

confidence: 99%

Manifestly covariant classical correlation dynamics II. Transport equations and Hakim equilibrium conjecture

Tian

2009

Ann. Phys.

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This is the second of a series of papers on special relativistic classical statistical mechanics. Employing the general theory developed in the first paper, we derive rigorously the relativistic Vlasov, Landau, and Boltzmann equations, respectively. The latter two equations advocate the Jüttner distribution as the equilibrium distribution. We thus, at the fully microscopic level, provide support for the recent numerical findings of Cubero and co-workers of the special relativistic generalization of the Maxwell-Boltzmann distribution. Furthermore, the present theory allows us to calculate rigorously various correlation functions at the relativistic many-body equilibrium. Therefore, we demonstrate that the relativistic many-body equilibrium conjecture of Hakim is justified.

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“…Then, a natural hope is to extend these concepts so as to suit relativity principles. At the early stages the Brussels-Austin school [15,45] undertook systematic attempts (see [13] for a review) to generalize the Newtonian classical correlation dynamics to special relativity, which is built on the canonical formulation of relativistic dynamics of classical many-body systems [8] with the Hamiltonian, if necessary, including field degrees of freedom. Unfortunately, as pointed out by many authors especially in the notable critical analysis by Hakim [1], Israel and Kandrup [18], and Kandrup [19], to proceed along this theoretical line one may have to overcome a number of conceptual and technical difficulties.…”

Section: Relativistic Nonequilibrium Statistical Mechanics: Manifestlmentioning

confidence: 99%

“…Indeed, in the development of old relativistic classical correlation dynamics a preferred time coordinate is chosen and then a Liouville equation is formulated building on the Hamiltonian formalism. Furthermore, in an insightful work Balescu and Kotera realized that in this framework the Lorentz invariance must be understood in terms of the Lorentz group action on the distribution functions of many-particle phase space (if www.ann-phys.org necessary, enlarged to accommodate field degrees of freedom) [13,45]. More precisely, the Lorentz group has 10 generators and in the group action representation the Liouvillian generates the time translation.…”

Section: Relativistic Nonequilibrium Statistical Mechanics: Manifestlmentioning

confidence: 99%

Manifestly covariant classical correlation dynamics I. General theory

Tian

2009

Ann. Phys.

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n this series of papers we substantially extend investigations of Israel and Kandrup on nonequilibrium statistical mechanics in the framework of special relativity. This is the first one devoted to the general mathematical structure. Basing on the action-at-a-distance formalism we obtain a single-time Liouville equation. This equation describes the manifestly covariant evolution of the distribution function of full classical many-body systems. For such global evolution the Bogoliubov functional assumption is justified. In particular, using the Balescu-Wallenborn projection operator approach we find that the distribution function of full many-body systems is completely determined by the reduced one-body distribution function. A manifestly covariant closed nonlinear equation satisfied by the reduced one-body distribution function is rigorously derived. We also discuss extensively the generalization to the general relativity especially an application to self-gravitating systems.Comment: 19 pages, 1 figure, substantially extende

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Lorentz symmetry of subdynamics in relativistic systems

Cited by 7 publications

References 11 publications

Laws of Nature and Time Symmetry Breaking

Laws of Nature and Time Symmetry Breaking

Manifestly covariant classical correlation dynamics II. Transport equations and Hakim equilibrium conjecture

Manifestly covariant classical correlation dynamics I. General theory

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