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Foundations of Physics

, Volume 19, Issue 12, pp 1441–1477 | Cite as

Quantum relativistic action at a distance

  • Donald C. Salisbury
  • Michael Pollot
Article

Abstract

A well-known relativistic action at a distance interaction of two unequal masses is altered so as to yield purely Newtonian radial forces with fixed particle rest masses in the system center-of-momentum inertial frame. Although particle masses experience no kinematic mass increase in this frame, speeds are naturally restricted to less than the speed of light. We derive a relation between the center-of-momentum frame total Newtonian energy and the composite rest mass. In a new proper time quantum formalism, we obtain an L2(R4 ⊗ R4, C) Hilbert space by varying individual particle rest masses. We propose the use of density operators, recognizing that the auxiliary proper time parameter is not an observable. The quantum formalism is applied to our altered version of the relativistic harmonic oscillator. Our generalized coherent states yield four-dimensional wave packets which follow the correct classical world lines. Appendices contain reviews of classical Hamiltonian reparametrization (incorporating our notion of manifest covariance), and a comparison of this work with the literature.

Keywords

Wave Packet Coherent State Density Operator Proper Time Inertial Frame 
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.

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References

  1. 1.
    D. G. Currie, T. F. Jordan, and E. C. G. Sudarshan,Rev. Mod. Phys. 35, 350 (1963).Google Scholar
  2. 2.
    M. Kalb and P. Van Alstine, “Invariant singular action for the relativistic two-body problem: A Hamiltonian formulation,” Yale, New Haven, Connecticut, 3075, 146 (1976).Google Scholar
  3. 3.
    M. Fujigaki and S. Kojima,Prog. Theor. Phys. 59, 1330 (1978).Google Scholar
  4. 4.
    T. Takabayashi,Prog. Theor. Phys. Suppl. 67, 1 (1979).Google Scholar
  5. 5.
    D. Dominici, J. Gomis, and G. Longhi,Nuovo Cimento 48A, 257 (1978).Google Scholar
  6. 6.
    R. Giachetti and E. Sorace,Nuovo Cimento 43A, 281 (1978).Google Scholar
  7. 7.
    J. A. Llosa, F. Marques, and A. Molina,Ann. Inst. H. Poincaré 32A, 303 (1980).Google Scholar
  8. 8.
    R. Arens,Arch. Rat. Mech. Anal. 47, 255 (1972).Google Scholar
  9. 9.
    I. T. Todorov, “Dynamics of relativistic point particles as a problem with constraints,”Commun. JINR EZ-10125 (unpublished), Dubna (1976).Google Scholar
  10. 10.
    Droz-Vincent,Ann. Inst. H. Poincare 27, 407 (1977).Google Scholar
  11. 11.
    A. Komar,Phys. Rev. D18, 1887 (1978).Google Scholar
  12. 12.
    F. Rohrlich,Ann. Phys. (N.Y.) 117, 292 (1979).Google Scholar
  13. 13.
    A. Kihlberg, R. Marnelius, and N. Mukunda,Phys. Rev. D23, 2202 (1981).Google Scholar
  14. 14.
    N. Mukunda and E. C. G. Sudarshan,Phys. Rev. D23, 2210 (1981).Google Scholar
  15. 15.
    E. C. G. Sudarshan, N. Mukunda, and J. Goldberg,Phys. Rev. D23, 2218 (1981).Google Scholar
  16. 16.
    L. Lusanna,Nuovo Cimento 65B, 135 (1981).Google Scholar
  17. 17.
    J. Llosa, ed.,Relativistic Action at a Distance: Classical and Quantum Aspects (Lecture Notes in Physics, Vol. 162) (Springer, Berlin, 1982).Google Scholar
  18. 18.
    V. Iranzo, J. Llosa, and A. Molina,Ann. Phys. (N.Y.) 150, 114 (1983).Google Scholar
  19. 19.
    E. C. G. Stueckelberg,Helv. Phys. Acta. 14, 588 (1941).Google Scholar
  20. 20.
    L. P. Horwitz and C. Piron,Helv. Phys. Acta. 46, 316 (1973).Google Scholar
  21. 21.
    L. P. Horwitz and Y. Rabin,Lett. Nuovo Cimento 17, 501 (1976).Google Scholar
  22. 22.
    L. P. Horwitz and F. C. Rotbart,Phys. Rev. D24, 2127 (1981).Google Scholar
  23. 23.
    R. Arshansky and L. P. Horwitz,Found. Phys.,15, 701 (1984).Google Scholar
  24. 24.
    L. P. Horwitz and F. Rohrlich,Phys. Rev. D23, 1305 (1981).Google Scholar
  25. 25.
    L. P. Horwitz and Y. Lavie,Phys. Rev. D26, 819 (1982).Google Scholar
  26. 26.
    L. P. Horwitz and F. Rohrlich,Phys. Rev. D26, 3452 (1982).Google Scholar
  27. 27.
    R. Arshansky, L. P. Horwitz, and Y. Lavie,Found. Phys. 13, 1167 (1983).Google Scholar
  28. 28.
    R. Arshansky and L. P. Horwitz,Phys. Lett. A128, 123 (1988).Google Scholar
  29. 29.
    T. D. Newton and E. P. Wigner,Rev. Mod. Phys. 21, 400 (1949).Google Scholar
  30. 30.
    E. Merzbacher,Quantum Mechanics (Wiley, New York, 1970).Google Scholar
  31. 31.
    M. J. King and F. Rohrlich,Ann. Phys. (N.Y.) 130, 350 (1980).Google Scholar
  32. 32.
    T. Takabayashi,Nuovo Cimento 33, 668 (1964).Google Scholar
  33. 33.
    Y. S. Kim and M. E. Noz.Phys. Rev. D8, 3521 (1973).Google Scholar
  34. 34.
    S. Ishida, A. Matsuda, and M. Namiki,Prog. Theor. Phys. 57, 210 (1977).Google Scholar
  35. 35.
    J. L. Anderson and P. G. Bergmann,Phys. Rev. 83, 1018 (1951); P. G. Bergmann and I. Goldberg,Phys. Rev. 98, 531 (1955).Google Scholar
  36. 36.
    P. A. M. Dirac,Can. J. Math. 2, 129 (1950); Lectures on Quantum Mechanics, Belfer Graduate School of Science Monographs Series, Yeshiva University (New York, 1964).Google Scholar
  37. 37.
    H. Crater and P. Van Alstine,Phys. Lett B100, 166 (1981).Google Scholar
  38. 38.
    T. Biswas,Nuovo Cimento A88, 145 (1985).Google Scholar
  39. 39.
    S. Ishida and K. Yamada, inHadron Spectroscopy-1985 (AIP Conference Proceedings No. 132) (American Institute of Physics, New York, 1985).Google Scholar
  40. 40.
    Y. K. Kwong, P. Prymmer and D. C. Salisbury, to appear.Google Scholar
  41. 41.
    K. Kyprianidis,Phys. Rep. 155, 1 (1987).Google Scholar
  42. 42.
    P. G. Bergmann and A. Komar,Int. J. Theor. Phys. 5, 15 (1972).Google Scholar
  43. 43.
    D. C. Salisbury and K. Sundermeyer,Phys. Rev. D27, 740 (1983).Google Scholar
  44. 44.
    D. C. Salisbury,Gen. Relativ. Gravit. 16, 955 (1984).Google Scholar
  45. 45.
    C. J. Isham and K. V. Kuchar,Ann. Phys. (N.Y.) 164, 288, 316 (1985).Google Scholar
  46. 46.
    K. V. Kuchar,Found. Phys. 16, 193 (1986).Google Scholar
  47. 47.
    D. Dominici, J. Gomis, and G. Longhi,Nuovo Cimento A56, 263 (1980).Google Scholar
  48. 48.
    D. Dominici, J. Gomis, and G. Longhi,Nuovo Cimento A66, 385 (1981).Google Scholar
  49. 49.
    M. J. King and F. Rohrlich,Ann. Phys. (N.Y.) 130, 350 (1081).Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • Donald C. Salisbury
    • 1
  • Michael Pollot
    • 2
  1. 1.Department of PhysicsAustin CollegeSherman
  2. 2.Department of PhysicsUniversity of TexasAustin

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