The multitime covariant formalism of relativistic dynamics

  • Ph. Droz-Vincent
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 162)


Phase Space Position Equation Canonical Variable Asymptotic Condition Liouville Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1).
    P. Droz-Vincent, Lett. Nuov. Cim., 1,839 (1969); Physica Scripta, 2,120(1970). for other manifestly covariant approaches seeGoogle Scholar
  2. 1a).
    J.G. Wray, Phys. Rev., D1, nº8,2212 (1970).Google Scholar
  3. 1b).
    R. Arens, Arch. for Rat. Mech. and Analysis, 47,255 (1972).CrossRefGoogle Scholar
  4. 1c).
    H.P. Künzle, J. Math. Phys., 15,1033 (1974). For the manifestly predictive formulation, see R.N. Hill, J. Math. Phys., 8,201(1967)CrossRefGoogle Scholar
  5. 1d).
    L. Bel, Ann. Inst. H. Poincaré, 12,307 (1970).Google Scholar
  6. 2).
    P. Droz-Vincent, Ann. Inst. H. Poincaré, XXVII, nº4,407 (1977) and Ref. C67.Google Scholar
  7. 3).
    D.G. Currie, J. Math. Phys., 4,1470 (1963); Phys. Rev., 142,817 (1966).CrossRefGoogle Scholar
  8. 3a).
    D.G. Currie, T.F. Jordan, E.C.G. Sudarshan, Rev. Mod. Phys., 35,350 (1963).CrossRefGoogle Scholar
  9. 3b).
    H. Leutwyler, Nuov. Cim., 37,556 (1965).Google Scholar
  10. 4).
    P. Droz-Vincent, Reports on Math. Phys., 8,nº1,79 (1975).CrossRefGoogle Scholar
  11. 5).
    Equations of motion like (1.10) have been written in P.A.M. Dirac, Comm. Dublin Inst. Adv. Studies, A º2 (1943). By that time Currie's theorem was not yet discovered and Dirac assumed that qa where the positions, which made his formulation correct for free particles only.Google Scholar
  12. 6).
    P. Droz-Vincent, Ann. Inst. H. Poincaré, A XXXII nº4,377(1980).Google Scholar
  13. 7).
    U. Mütze, J. Math. Phys., 9,231 (1978).CrossRefGoogle Scholar
  14. 8).
    L. Bel, X. Fustero, Ann. Inst. H. Poincaré, 24,411 (1976). P. Droz-Vincent, Ref.[6]. V. Iranzo, J. Llosa, F. Marques, A. Molina, to be published in Ann. Inst. H. Poincaré 1981.Google Scholar
  15. 9).
    F. Rohrlich, Phys. Rev. D, 23, nº6,1305 (1981).CrossRefGoogle Scholar
  16. 10).
    H. Sazdjian, Orsay preprint IPNO/TH 80–38 (Sept. 80) and (Janv.81).Google Scholar
  17. 11).
    V.V. Molotkov, I.T. Todorov, Comm. Math. Phys., 79,111 (1981). I.T. Todorov, to be published.CrossRefGoogle Scholar
  18. 12).
    P. Droz-Vincent, Lecture from Unesco Colloquium, Paris (June 1977).Google Scholar
  19. 13).
    J. Llosa, A. Marqués, A. Molina, Ann. Inst. H. Poincaré, XXXII, nº4,363 (1980).Google Scholar
  20. 13a).
    D. Dominici, J. Gomis, J.A. Lobo, J.M. Pons, Nuov. Cim., 61B nº2, 306 (19813).Google Scholar
  21. 14).
    K. Kamimura, T. Shimizu, Prog. Theor. Phys., 58,383 (1977).Google Scholar
  22. 14a).
    M. Fujigaki, S. Kojima, Prog. Theor. Phys., 59,1330 (1978).Google Scholar
  23. 14b).
    D. Dominici, J. Gomis, G. Longhi, Nuov. Cim., 148,257 (1978); Nuov. Cim., B48,152(1978).Google Scholar
  24. 14c.
    S. Kojima, Prog. Theor. Phys., 61,960 (1979).Google Scholar
  25. 15).
    L. Lusanna, Il Nuovo Cimento 65B, nº1, 135 (1981).Google Scholar
  26. 16).
    E.H. Kerner, R.N. Hill, Phys. Rev. Lett., 17,1156 (1966).Google Scholar
  27. 16a).
    R.N. Hill, J. Math. Phys., 8,1756 (1967); J. Math.Phys., 11, 1918 (1970).CrossRefGoogle Scholar
  28. 17).
    L. Bel, J. Martin, Ann. Inst. H. Poincaré, XXII nº3,173 (1975).Google Scholar
  29. 18).
    S. Ohełkowski,J. Nietendel, R. Suchanek, Acta Phys. Polon. B nº11, 809 (1980).Google Scholar
  30. 19).
    For details about calculations in single-potentials two-body systems see Ref. [2].Google Scholar
  31. 20).
    P. Droz-Vincent, C.R. Acad. Sc. Paris, 292,239(1981). Beware that the statement (+) in this note must be corrected. Hence the solution remains (so far) formal.Google Scholar
  32. 21).
    V. Iranzo, J. Llosa, F. Marques, A. Molina, Ann. Inst. H. Poincaré, to be published.Google Scholar
  33. 22).
    L. Lusanna, Ref.[15] eq. (7.14) et (7.15). Our θ,,θ2,are a case of Lusanna sP4, P2.Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Ph. Droz-Vincent
    • 1
  1. 1.Chaire de Physique MathématiqueCollege de FranceCedex 05Paris

Personalised recommendations