International Journal of Theoretical Physics

, Volume 12, Issue 5, pp 299–320 | Cite as

Crossing relations derived from (Extended) Relativity

  • R. Mignani
  • E. Recami
Article

Abstract

Recently, Special Relativity has been straightforwardly extended to Superluminal inertial frames and faster-than-light objects. The ‘Extended Relativity’ theory not only allowed building up a self-consistent ‘classical theory’ of tachyons, but reveals itself useful also for the understanding of standard (subluminal) physics, i.e. of usual particles. In this paper, it is shown that Extended Relativity allows: (i) deriving the usual ‘Crossing Relations’ of elementary particle (high-energy) physics; and (ii) deriving the CPT-covariance theorem as a particular case of G-covariance (i.e., covariance under the new group of Generalised Lorentz transformations, both subluminal and Superluminal).

In this framework, the ‘Analyticity’ postulate is unnecessary: it is better substituted by the G-covariance requirement.

Moreover, new ‘crossing-type’ relations are predicted on the basis of mere Extended Relativity. They may well serve as a test for relativistic covariance of ‘force fields’ like strong interactions and, particularly, weak interactions, and possible new ‘interaction fields’ (whicha priori are not relativistically covariant).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agodi, A. (1973).Lectures in Theoretical Physics, Catania, unpublished.Google Scholar
  2. Antippa, A. F. and Everett, A. E. (1973).Physical Review,8, 2352.Google Scholar
  3. Arons, M. E. and Sudarshan, E. C. G. (1968).Physical Review,173, 1622.Google Scholar
  4. Atkinson, D. A. (1973). Preprint, Tekn. Technology Univ.Google Scholar
  5. Baldo, M. and Recami, E. (1969).Letters Nuovo Cimento,2, 643.Google Scholar
  6. Baldo, M., Fonte, G. and Recami, E. (1970).Letters Nuovo Cimento,4, 241.Google Scholar
  7. Berestetsky, V., Lifshitz, E. M. and Pitaevsky, P. (1971).Relativistic Quantum Theory, p. 34. London.Google Scholar
  8. Bilaniuk, O. M. P., Deshpande, V. K. and Sudarshan, E. C. G. (1962).American Journal of Physics,30, 718.Google Scholar
  9. Chew, G. (1962).S-Matrix Theory of Strong Interactions, Benjamin Pub., N.Y.Google Scholar
  10. Csonka, P. L. (1969).Physical Reviews,180, 1266.Google Scholar
  11. Dhar, T. and Sudarshan, E. C. G. (1968).Physical Review,174, 1808.Google Scholar
  12. Dirac, P. A. M. (1930).Proceedings of the Royal Society (London) A126, 360.Google Scholar
  13. Fabri, E. (1959).Nuovo Cimento,14, 1130.Google Scholar
  14. Feinberg, G. (1967).Physical Review,159, 1089.Google Scholar
  15. Ferretti, I. and Verde, M. (1966).Atti dell'Accademia delle scienze. Torino, p. 318. Verde, M. (unpublished).Google Scholar
  16. Feynamn, R. P. (1949).Physical Review,76, 749, 769.Google Scholar
  17. Gleeson, A. M., Gundzik, M. G., Sudarshan, E. C. G. and Pagnamenta, A. (1972).Physical Review,D6, 807.Google Scholar
  18. Glück, M. (1969).Nuovo Cimento,A62, 791.Google Scholar
  19. Goldoni, R. (1973).Nuovo Cimento,A14, 501.Google Scholar
  20. Hadjioannou, F. T. (1966).Nuovo Cimento,44, 185.Google Scholar
  21. Hagedorn, R. (1963).Relativistic Kinematics, Benjamin Pub.Google Scholar
  22. Lee, T. D. and Yang, C. N. (1957).Physical Review,105, 1671.Google Scholar
  23. Messiah, A. (1965).Quantum Mechanics, Volume I, Chapter 10. North-Holland Pub., Amsterdam.Google Scholar
  24. Mignani, R. and Recami, E. (1973a). ‘Classical Theory of Tachyons (Special Relativity Extended to Superluminal Frames and Objects)’, preprint IFTUC-PP/387, Catania, to appear inRivista Nuovo Cimento, and references therein.Google Scholar
  25. Mignani, R. and Recami, E. (1973b).Nuovo Cimento,A14, 169.Google Scholar
  26. Mignani, R. and Recami, E. (1973c).Nuovo Cimento,A16, 208.Google Scholar
  27. Mignani, R. and Recami, E. (1973d).Letters Nuovo Cimento,7, 388;8, 780;9, 362, 367, 479;11, 417;Nuovo Cimento,B21, 210.Google Scholar
  28. Olkhovsky, V. S. and Recami, E. (1969).Nuovo Cimento,A63, 814.Google Scholar
  29. Olkhovsky, V. S. and Recami, E. (1971).Letters Nuovo Cimento,1, 165.Google Scholar
  30. Parker, L. (1969).Physical Review,188, 2287.Google Scholar
  31. Pauli, W. (1921).Relativitätstheorie, Leipzig.Google Scholar
  32. Recami, E. (1969a).Giornale di Fisica,10, 195.Google Scholar
  33. Recami, E. (1970).Atti dell'Accademia nazionale dei Lincei. Rendiconti,49, 77.Google Scholar
  34. Recami, E. (1973). I Tachioni, inEnciclopedia EST-Mondadori, Annuario 73, p. 85. Milano.Google Scholar
  35. Recami, E. and Mignani, R. (1972).Letters Nuovo Cimento,4, 144.Google Scholar
  36. Recami, E. and Mignani, R. (1973).Letters Nuovo Cimento,8, 110.Google Scholar
  37. Recami, E. and Mignani, R. (1974).Rivista Nuovo Cimento,4, 209, 398, and references therein.Google Scholar
  38. Roman, P. (1969).Introduction to Quantum Field Theory, J. Wiley Inc., New York.Google Scholar
  39. Sakurai, J. J. (1964).Invariance Principles and Elementary Particles, p. 137. Princeton.Google Scholar
  40. Sakurai, J. J. (1964).Invariance Principles and Elementary Particles, Chapter 7. Princeton.Google Scholar
  41. Stückelberg, E. C. G. (1941).Helvetica Physica Acta,14, 32L, 588.Google Scholar
  42. Sudarshan, E. C. G. (1968).Proceedings of the Indian Academy of Sciences,67(5A), 284.Google Scholar
  43. Sudarshan, E. C. G. (1969a).Arkiv für Physik,39(40), 585.Google Scholar
  44. Sudarshan, E. C. G. (1969b).Proceedings of the Indian Academy of Sciences,69(3A, 133; and in1968 Proceedings of the VIII Nobel Symposium (Elementary Particle Theory), Swartholm, N. ed., p. 335. J. Wiley Pub., New York and Almqvist and Wiksell Pub., Stockholm.Google Scholar
  45. Sudarshan, E. C. G. (1970). inSymposia in Theor. Phys. and Math. Vol. 10, p. 129, Plenum Press.Google Scholar
  46. Sudarshan, E. C. G. (1972). Preprint CPT-166, Austin; (1968). Preprint NYO-3399-191/SU-1206-191, Syracuse.Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • R. Mignani
    • 1
    • 2
  • E. Recami
    • 1
    • 2
  1. 1.Istituto di Fisica TeoricaUniversità di CataniaCataniaItaly
  2. 2.Istituto Nazionale di Fisica NucleareSezione di Catania. Centro Siciliano di Fisica Nucleare e di Struttura della MateriaCatania

Personalised recommendations