Abstract
We discuss questions related to the well-posedness of problems on the motion of relativistic many-body systems. For one-dimensional relativistic motion of N similar charges, we prove that an ordinary Cauchy problem usual in Newton mechanics can be stated; this is done in the framework of microscopic Maxwell-Lorentz electrodynamics (including a model with self-action) or Wheeler-Feynman theory.
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C. M. Andersen and H. C. von Baeyer, “Almost circular orbits in classical action-at-a-distance electrodynamics,” Phys. Rev. D, 5, No. 4, 802–813 (1972).
W. E. Baylis and J. Huschilt, “Numerical solutions to two-body problems in classical electrodynamics: straight-line motion with retarded fields and no radiation reaction,” Phys. Rev. D, 7, No. 10, 2844–2850 (1973).
C. G. Darvin, Philos. Mag., 39, 537 (1920).
P. A. M. Dirac, “Classical theory of radiating electrons,” Proc. Roy. Soc. London, Ser. A, 167, 148–168, (1938).
R. D. Driver, “A ‘backwards’ two-body problem of classical relativistic electrodynamics,” Phys. Rev., 178, No. 5, 2051–2057 (1969).
R. D. Driver, “Can the future influence the present?” Phys. Rev. D, 19, No. 4, 1098–1107 (1979).
R. D. Driver and D. K. Hsing, in: Dynamical Systems, Proc. Int. Symp.Univ. Florida, Academic Press, New York (1977), pp. 427–430.
J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Appl. Math. Sci., 99, Springer-Verlag, New York (1993).
D. K. Hsing, “Existence and uniquence theorem for the one-dimentional backwards two-bodies problem of electrodynamics,” Phys. Rev. D, 16, 974–982 (1977).
A. D. Myshkis, Linear Differential Equations with Retarded Arguments [in Russian], Nauka, Moscow (1972).
G. N. Plass, “Classical electrodynamic equations of motion with radiative reaction,” Rev. Mod. Phys., 33, No. 1, 37–62 (1961).
A. Schild, “Electromagnetic two-body problem,” Phys. Rev., 131, No. 6, 2762–2766 (1963).
J. L. Synge, “On the electromagnetic two-bodies problem,” Proc. Roy. Soc. London, Ser. A, 177, 118–199, (1941).
H. Van Dam and E. P. Wigner, “Classical relativistic mechanics of interacting point particles,” Phys. Rev., 138, No. 6b, 1576–1582 (1965).
J. A. Wheeler and R. P. Feynman, “Interaction with the absorber as the mechanism of radiation,” Rev. Mod. Phys., 17, 157–181 (1945).
J. A. Wheeler and R. P. Feynman, “Classical electrodynamics in terms of direct interparticle action,” Rev. Mod. Phys., 21, 425–433 (1949).
V. I. Zhdanov, “On the one-dimentional symmetric two-body problem of classical electrodynamics,” Int. J. Theor. Phys., 15, No. 2, 157–167 (1976).
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Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry, 2005.
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Kirpichev, S.B., Polyakov, P.A. On the formulation of initial-value problems for systems consisting of relativistic particles. J Math Sci 141, 1051–1061 (2007). https://doi.org/10.1007/s10958-007-0032-6
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DOI: https://doi.org/10.1007/s10958-007-0032-6