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Teoreticheskaya i Matematicheskaya Fizika, 1980, Volume 44, Number 2, Pages 194–208 (Mi tmf3495)  

This article is cited in 16 scientific papers (total in 16 papers)

Lagrangian classical relativistic mechanics of a system of directly interacting particles. I

R. P. Gaida, Yu. B. Klyuchkovskii, V. I. Tretyak
References:
Abstract: General formulation of the one-time Lagrangian relativistic classical description of N directly interacting particles is developed. A representation of a continuous transformation group of the Minkowski space (in particular, Poincare group) by the Lie–Backlund tangent transformations of the configuration space of the system is constructed. By means of this representation the system of linear differential equations expressing the Poincare invariance of the Lagrangian formalism is obtained and corresponding restrictions on the form of the generalised Lagrangian are studied. The exact relativistic description of the interaction is shown to demand the dependence of the Lagrangian on the infinite order derivatives. The results will be used in the second part of the work for finding a general form of the approximate relativistic interaction Lagrangian and for working out the method of constructing the Poincare invariant Newton type equations of motion and their first integrals.
Received: 23.05.1979
English version:
Theoretical and Mathematical Physics, 1980, Volume 44, Issue 2, Pages 687–697
DOI: https://doi.org/10.1007/BF01018448
Bibliographic databases:
Language: Russian
Citation: R. P. Gaida, Yu. B. Klyuchkovskii, V. I. Tretyak, “Lagrangian classical relativistic mechanics of a system of directly interacting particles. I”, TMF, 44:2 (1980), 194–208; Theoret. and Math. Phys., 44:2 (1980), 687–697
Citation in format AMSBIB
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\paper Lagrangian classical relativistic mechanics of~a~system of~directly interacting particles.~I
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\vol 44
\issue 2
\pages 194--208
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=587300}
\transl
\jour Theoret. and Math. Phys.
\yr 1980
\vol 44
\issue 2
\pages 687--697
\crossref{https://doi.org/10.1007/BF01018448}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1980LL99100005}
Linking options:
  • https://www.mathnet.ru/eng/tmf3495
  • https://www.mathnet.ru/eng/tmf/v44/i2/p194
    Cycle of papers
    This publication is cited in the following 16 articles:
    1. Jörn Dunkel, Peter Hänggi, “Relativistic Brownian motion”, Physics Reports, 471:1 (2009), 1  crossref
    2. Horace Crater, Luca Lusanna, “The Rest-Frame Darwin Potential from the Lienard–Wiechert Solution in the Radiation Gauge”, Annals of Physics, 289:2 (2001), 87  crossref
    3. DAVID ALBA, LUCA LUSANNA, “THE LIENARD–WIECHERT POTENTIAL OF CHARGED SCALAR PARTICLES AND THEIR RELATION TO SCALAR ELECTRODYNAMICS IN THE REST-FRAME INSTANT FORM”, Int. J. Mod. Phys. A, 13:16 (1998), 2791  crossref
    4. Roman Gaida, Volodymyr Tretyak, “Symmetries of the Fokker-Type Relativistic Mechanics in Various Forms of Dynamics”, JNMP, 3:3-4 (1996), 357  crossref
    5. R. A. Moore, T. C. Scott, “Causality and quantization of time-delay systems: A two-body model problem”, Phys. Rev. A, 52:6 (1995), 4371  crossref
    6. R. A. Moore, T. C. Scott, “Causality and quantization of time-delay systems: A model problem”, Phys. Rev. A, 52:3 (1995), 1831  crossref
    7. R. P. Gaida, V. I. Tretyak, Yu. G. Yaremko, “Center-of-mass variables in the relativistic Lagrangian dynamics of a system of particles”, Theoret. and Math. Phys., 101:3 (1994), 1443–1453  mathnet  crossref  mathscinet  zmath  isi
    8. R. A. Moore, T. C. Scott, “Quantization of second-order Lagrangians: The Fokker-Wheeler-Feynman model of electrodynamics”, Phys. Rev. A, 46:7 (1992), 3637  crossref
    9. Thibault Damour, Gerhard Schäfer, “Redefinition of position variables and the reduction of higher-order Lagrangians”, Journal of Mathematical Physics, 32:1 (1991), 127  crossref
    10. R. P. Gaida, Yu. B. Klyuchkovskii, V. I. Tretyak, “Group-theoretic approach to the construction of relativistic lagrangian mechanics of a system of particles”, Ukr Math J, 43:11 (1991), 1408  crossref
    11. R. P. Gaida, Yu. B. Klyuchkovskii, V. I. Tretyak, “Relativistic theory of direct interactions and gravitational two-body problem in the second post-Newtonian approximation”, Soviet Physics Journal, 33:1 (1990), 40  crossref
    12. R. P. Gaida, V. I. Tretyak, “Lagrangian of two charged gravitating bodies in the second post-Newton approximation”, Soviet Physics Journal, 33:7 (1990), 575  crossref
    13. S. N. Sokolov, V. I. Tretyak, “Front form of relativistic Lagrangian dynamics in two-dimensional space-time and its connection with the Hamiltonian description”, Theoret. and Math. Phys., 67:1 (1986), 385–394  mathnet  crossref  mathscinet  isi
    14. R. P. Gaida, Yu. B. Klyuchkovskii, V. I. Tretyak, “Forms of relativistic dynamics in a classical Lagrangian description of a system of particles”, Theoret. and Math. Phys., 55:1 (1983), 372–384  mathnet  crossref  mathscinet  isi
    15. F. M. Lev, “On a Three-Body Problem in Relativistic Quantum Mechanics”, Fortschr. Phys., 31:2 (1983), 75  crossref
    16. R. P. Gaida, Yu. B. Klyuchkovskii, V. I. Tretyak, “Lagrangian classical relativistic mechanics of a system of directly interacting particles. II”, Theoret. and Math. Phys., 45:2 (1980), 963–975  mathnet  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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