International Journal of Theoretical Physics

, Volume 32, Issue 11, pp 2087–2098 | Cite as

Canonical proper time formulation of relativistic particle dynamics

  • Tepper Gill
  • James Lindesay
Article

Abstract

A canonical (contact) transformation is performed on the time variable (in extended phase space) to reexpress relativistic dynamics in terms of proper time, leaving the generalized coordinates and canonical momentum as functions of this time variable. The form of the energy functional conjugate to this time variable is seen to be similar to that of a nonrelativistic dynamics at all values of particle momenta. The formulation is explored for single- and multiparticle classical systems. The (form) invariance of the theory is determined by a group which results from a similarity action of the contact group on the Poincaré group. One advantage of this approach is that it overcomes the no-interaction difficulties introduced by standard methods.

Keywords

Field Theory Phase Space Elementary Particle Quantum Field Theory Time Variable 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arnold, V. I. (1978).Mathematical Methods of Classical Mechanics, Springer-Verlag, New York.Google Scholar
  2. Currie, D. G. (1963).Journal of Mathematical Physics,4.Google Scholar
  3. Currie, D. G., Jordan, T. F., and Sudarshan, E. C. G. (1963).Review of Modern Physics,35.Google Scholar
  4. Davis, P. C. W. (1970).Proceedings of the Cambridge Philosophical Society,68, 751.Google Scholar
  5. Dirac, P. A. M. (1977).Mathematical Foundations of Quantum Theory, Academic Press, New York.Google Scholar
  6. Einstein, A. (1905a).Annalen der Physik,17, 891.Google Scholar
  7. Einstein, A. (1950b).Annalen der Physik,18, 639.Google Scholar
  8. Gill, T. L. (1982). Fermilab-Pub-82/60-THY.Google Scholar
  9. Hoyle, F., and Narlikar, J. V. (1969).Annals of Physics,54, 207.Google Scholar
  10. Kerner, E. H. (1972).The Theory of Action-at-a-Distance in Relativistic Particle Dynamics, Gordon and Breach, New York.Google Scholar
  11. Longhi, G., and Lusanna, L. (1986).Physical Review D,34, 3707.Google Scholar
  12. Longhi, G., Lusanna, L., and Pons, J. M. (1989).Journal of Mathematical Physics,30, 1893.Google Scholar
  13. Lorentz, H. A. (1892).Archives Neerlandaises des Sciences Exactes et Naturelles,25, 353.Google Scholar
  14. Lorentz, H. A. (1903). InEnzyklopädie der Mathematischen Wissenschaften, Vol. 1, p. 188.Google Scholar
  15. Maxwell, J. C. (1865).Philosophical Transactions of the Royal Society of London,155, 459.Google Scholar
  16. Maxwell, J. C. (1891).Treatise on Electricity and Magnetism, 3rd ed. [reprint, Dover, NewYork, 1954].Google Scholar
  17. Newton, I. (1966).Philosophiae Naturalis Principia Mathematica, translated by Andrew Motts, revised and annotated by F. Cajori, University of California Press, Berkeley, California.Google Scholar
  18. Pegg, D. T. (1979).Annals of Physics,118, 1.Google Scholar
  19. Pryce, M. H. L. (1948).Proceedings of the Royal Society of London, Series A,195, 400.Google Scholar
  20. Ritz, W. (1908a).Annales de Chimie et de Physique,13, 145.Google Scholar
  21. Ritz, W. (1908b).Archives des Sciences Physiques et Naturelles,16, 209.Google Scholar
  22. Ritz, W. (1912).Physikalische Zeitschrift,13, 317.Google Scholar
  23. Rohrlich, F. (1979).Annals of Physics,117, 292.Google Scholar
  24. Rosen, G. (1969).Foundations of Classical and Quantum Dynamical Theory, Academic Press, New York.Google Scholar
  25. Tolman, R. C. (1910a).Physical Review,30, 291.Google Scholar
  26. Tolman, R. C. (1910b).Physical Review,31, 26.Google Scholar
  27. Van-Dam, H., and Wigner, E. P. (1965).Physical Review,138, B1576.Google Scholar
  28. Van-Dam, H., and Wigner, E. P. (1966).Physical Review,142, B838.Google Scholar
  29. Wheeler, J. A., and Feynman, R. P. (1945).Review of Modern Physics,17, 157.Google Scholar
  30. Wheeler, J. A., and Feynman, R. P. (1949).Review of Modern Physics,21, 425.Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • Tepper Gill
    • 1
  • James Lindesay
    • 2
  1. 1.Department of Electrical EngineeringHoward UniversityWashington, D.C.
  2. 2.Department of PhysicsHoward UniversityWashington, D.C.

Personalised recommendations