On the formulation of initial-value problems for systems consisting of relativistic particles

Kirpichev, Sergey B; Polyakov, P. A.

doi:10.1007/s10958-007-0032-6

Cited by 6 publications

(14 citation statements)

References 15 publications

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“…A statistical theory based on this formalism, in turn, is expected to explain this numerical finding. (ii) The Kirpichev-Polyakov theorem [5] partly justifies the longstanding conjecture of Hakim on mathematical foundations of relativistic statistical mechanics [1]. It is shown that for 1-dimensional relativistic dynamics of classical charged systems, which is formulated in terms of the Wheeler-Feynman formalism [7], an ordinary Cauchy problem as in the Newtonian mechanics can be stated.…”

Section: Overview Of This Series Of Papersmentioning

confidence: 77%

“…The fundamental problem of physics of relativistic classical many-body systems is one century old (for a review of early investigations see, e.g., [1]) and, still, remains one of the most important subjects in studies of relativity [2][3][4][5]. At the microscopic level the basis of deterministic classical dynamics of relativistic many-body systems has been widely explored [6][7][8][9].…”

Section: Some Motivationsmentioning

confidence: 99%

“…Furthermore, all the microscopic states constitute the space Ω N which has the dimensionality ≥ 8N . (A nontrivial example is presented in [5], where the equality holds.) Given a bundle of N particle world lines satisfying Eq.…”

Section: Manifestly Covariant Single-time Liouville Equationmentioning

confidence: 99%

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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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Section: Overview Of This Series Of Papersmentioning

confidence: 77%

Section: Some Motivationsmentioning

confidence: 99%

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Manifestly covariant classical correlation dynamics I. General theory

Tian

2009

Ann. Phys.

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“…(There do exist exceptions, for example, the case studied in Ref. [42].) Indeed, the introduction of the Γ phase space is merely suggested by the form of the motion equations.…”

Section: Discussionmentioning

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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“…For clarity, we first focus on the point-particle case, where the self-force is neglected, but the situation is still relativistic, i.e. retardation effects are essential [52][53][54][55][56][57][58][59][60]. In this situation particles influence each other via the Lorentz forces generated by the Lienard-Wichert potentials; see Appendix F.…”

Section: Two Point-particles Without Self-interactionsmentioning

confidence: 99%

Electromagnetic gauge-freedom and work

Allahverdyan¹,

Babajanyan²

2016

J. Phys. A: Math. Theor.

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We argue that the definition of the thermodynamic work done on a charged particle by a timedependent electromagnetic field is an open problem, because the particle's Hamiltonian is not gaugeinvariant. The solution of this problem demands accounting for the source of the field. Hence we focus on the work done by a heavy body (source) on a lighter particle when the interaction between them is electromagnetic and relativistic. The work can be defined via the gauge-invariant kinetic energy of the source. We uncover a formulation of the first law (or the generalized work-energy theorem) which is derived from relativistic dynamics, has definite validity conditions, and relates the work to the particle's Hamiltonian in the Lorenz gauge. Thereby the thermodynamic work also relates to the mechanic work done by the Lorentz force acting on the source. The formulation of the first law is based on a specific separation of the overall energy into those of the source, particle and electromagnetic field. This separation is deduced from a consistent energy-momentum tensor. Hence it holds relativistic covariance and causality.

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On the formulation of initial-value problems for systems consisting of relativistic particles

Cited by 6 publications

References 15 publications

Manifestly covariant classical correlation dynamics I. General theory

Manifestly covariant classical correlation dynamics I. General theory

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

Electromagnetic gauge-freedom and work

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