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Pramana

, Volume 22, Issue 3–4, pp 131–150 | Cite as

Relativistic particle interactions—A comparison of independent and collective variable models

  • J Samuel
  • N Mukunda
Quantum Mechanics
  • 21 Downloads

Abstract

We present a detailed comparison of two models for relativistic classical particle interactions recently discussed in the literature—one based on independent particle variables, and the other on centre of mass plus relative variables. Basic to a meaningful comparison is a reformulation of the latter model which shows that it makes essential use of the concept of invariant relations from constrained Hamiltonian theory. We conclude that these two models have very different physical and formal structures and cannot be thought of as two equivalent descriptions of the same physical theory.

Keywords

Hamiltonian relativistic mechanics constrained Hamiltonian dynamics relativistic particle mechanics relativistic particle interactions 

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References

  1. Balachandran A, Marmo G, Mukunda N, Nilsson J S, Simoni A, Sudarshan E C G and Zaccaria F 1982aNuovo Cimento A67 121MathSciNetGoogle Scholar
  2. Balachandran A, Marmo G, Mukunda N, Nilsson J S, Simoni A, Sudarshan E C G and Zaccaria F 1982bUnified geometrical approach to relativistic particle dynamics Preprint DOE-ER-03992-489, CPT, University of Texas at AustinGoogle Scholar
  3. Balachandran A, Dominici D, Marmo G, Mukunda N, Nilsson J S, Samuel J, Sudarshan E C G and Zaccaria F 1982cPhys. Rev. D26 3492ADSMathSciNetGoogle Scholar
  4. Cannon J T and Jordan T F 1964J. Math. Phys. 5 299MATHCrossRefADSMathSciNetGoogle Scholar
  5. Currie D G, Jordan T F and Sudarshan E C G 1963Rev. Mod. Phys. 35 350CrossRefADSMathSciNetGoogle Scholar
  6. Dirac P A M 1949Rev. Mod. Phys. 21 392MATHCrossRefADSMathSciNetGoogle Scholar
  7. Dominici D, Gomis J and Longhi G 1978aNuovo Cimento A48 257Google Scholar
  8. Dominici D, Gomis J and Longhi G 1978bNuovo Cimento B48 152Google Scholar
  9. Hsu J P and Shi T Y 1982Phys. Rev. D26 2745ADSMathSciNetGoogle Scholar
  10. Iranzo V, Llosa J, Molina A and Marques F 1982Comparison of several approaches to the relativistic dynamics of directly interacting particles Preprint, University of Barcelona FT 5–82Google Scholar
  11. Kihlberg A, Marnelius R and Mukunda N 1981Phys. Rev. D23 2201ADSMathSciNetGoogle Scholar
  12. King M J and Rohrlich F 1980Ann. Phys. (N. Y.) 130 350CrossRefADSMathSciNetGoogle Scholar
  13. Komar A 1978aPhys. Rev. D18 1881ADSMathSciNetGoogle Scholar
  14. Komar A 1978bPhys. Rev. D18 1887ADSMathSciNetGoogle Scholar
  15. Komar A 1978cPhys. Rev. D18 3617ADSMathSciNetGoogle Scholar
  16. Leutwyler H 1965Nuovo Cimento 37 556CrossRefGoogle Scholar
  17. Mukunda N and Sudarshan E C G 1981Phys. Rev. D23 2210ADSMathSciNetGoogle Scholar
  18. Rohrlich F 1979aAnn. Phys. (N.Y.) 117 292CrossRefADSMathSciNetGoogle Scholar
  19. Rohrlich F 1979bPhysica A96 290ADSGoogle Scholar
  20. Samuel J 1982aPhys. Rev. D26 3475ADSMathSciNetGoogle Scholar
  21. Samuel J 1982bPhys. Rev. D26 3482ADSMathSciNetGoogle Scholar
  22. Samuel J 1984 Work in preparationGoogle Scholar
  23. Sudarshan E C G, Mukunda N and Goldberg J N 1981Phys. Rev. D23 2218ADSMathSciNetGoogle Scholar
  24. Todorov I T 1971Phys. Rev. D3 2351ADSGoogle Scholar
  25. Todorov I T 1976Commun. JINR E.2-10125 DubnaGoogle Scholar

Copyright information

© Indian Academy of Sciences 1984

Authors and Affiliations

  • J Samuel
    • 1
  • N Mukunda
    • 1
    • 2
  1. 1.Raman Research InstituteBangaloreIndia
  2. 2.Centre for Theoretical Studies and Department of PhysicsIndian Institute of ScienceBangaloreIndia

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