International Journal of Theoretical Physics

, Volume 2, Issue 3, pp 201–211 | Cite as

Causality restrictions on relativistic extensions of particle symmetries

  • P. Roman
  • R. M. Santilli


Relativistic extensions of internal hadron symmetry groups are investigated from the viewpoint of causality requirements. Zeeman's group theoretical definition of causality is adopted and various physically interesting structures of relativistic extensions are studied from the viewpoint of whether they preserve or violate causality. Four theorems that guarantee causality preservation, and three theorems that violate it are deduced. It is concluded that there does not exist a non-trivial coupling of the Poincaré group and an internal symmetry group, such asSU(3) orSU(6), preserving causality in a Minkowski space. Extensions in complex or in curved manifolds are briefly discussed.


Manifold Field Theory Elementary Particle Quantum Field Theory Symmetry Group 
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  1. Barut, A. O. (1964).Lectures in Theoretical Physics, Vol. VIIa. Boulder.Google Scholar
  2. Bohm, A. (1967).Physical Review,158, 1408.Google Scholar
  3. Castell, L. (1968).Nuclear Physics,5, B601.Google Scholar
  4. Coester, F., Hamermesh, M. and McGlinn, W. D. (1964).Physical Review,135, B451.Google Scholar
  5. Coleman, S. and Mandula, J. (1967).Physical Review,159, 1251.Google Scholar
  6. Doebner, H. D. and Melsheimer, O. (1966). Nato International Advanced Study Institute, Istanbul.Google Scholar
  7. Fleischman, O. and Nagel, J. G. (1967).Journal of Mathematics and Physics,7, 1128.Google Scholar
  8. Formanek, J. (1966).Czechoslovak Journal of Physics,B16, 1, 281.Google Scholar
  9. Gantmacher, F. (1939).Matematische Sitzungberichte,5 (47), 101, 218.Google Scholar
  10. Greenberg, O. W. (1964).Physical Review,135, B1447.Google Scholar
  11. Helgason, S. (1962).Differential Geometry and Symmetric Spaces. Academic Press.Google Scholar
  12. Hergfeldt, C. G. and Hennig, J. (1969).Fortschritte der Physik. In press.Google Scholar
  13. Iwasawa, K. (1949).Annals of Mathematics,50, 507.Google Scholar
  14. Jost, R. (1966).Helvetica Physica acta,39, 369.Google Scholar
  15. Kihlberg, A., Müller, V. F. and Halbwachs, F. (1966).Communication in Mathematical Physics,3, 194.Google Scholar
  16. McGlinn, W. D. (1964).Physical Review Letters,12, 467.Google Scholar
  17. Michel, L. (1965).Physical Review,137, B405.Google Scholar
  18. Mugibayashi, N. (1966).Progress of Theoretical Physics,35, 315.Google Scholar
  19. Nakamura, M. (1967).Progress of Theoretical Physics,37, 195.Google Scholar
  20. Onišcik, A. L. (1966).American Mathematical Society Translations, (2)50, 235.Google Scholar
  21. Ottoson, U., Kihlberg, A. and Nilsson, J. (1965).Physical Review,137, B658.Google Scholar
  22. O'Raifeartaigh, L. (1965a).Physical Review Letters,14, 575.Google Scholar
  23. O'Raifeartaigh, L. (1956).Physical Review,139, 1052.Google Scholar
  24. O'Raifeartaigh, L. (1967a).Physical Review,161, 1571.Google Scholar
  25. O'Raifeartaigh, L. (1967b).Physical Review,164, 2000.Google Scholar
  26. Roman, P. and Koh, C. J. (1965).Nuovo cimento,39, 1015.Google Scholar
  27. Roman, P. and Aghassi, J. J. (1966).Journal of Mathematical Physics,7, 1273, and papers quoted therein.Google Scholar
  28. Roskies, R. (1966).Journal of Mathematical Physics,7, 395.Google Scholar
  29. Santilli, R. M. (1968a).Nuovo cimento,55, B578.Google Scholar
  30. Santilli, R. M. (1968b). Contributed paper to the Indiana Symposium, Bloomington, to appear in the Proceedings, to be published by Gordon and Breach.Google Scholar
  31. Santilli, R. M. (1968c).Supplemento al Nuovo Cimento,4, 1225.Google Scholar
  32. Segal, I. (1967).Proceedings of the National Academy of Sciences of the United States of America,57, 294.Google Scholar
  33. Toller, M. (1968).Symmetry Principles at High Energy. W. A. Benjamin, Inc., Coral Gables.Google Scholar
  34. Wegal, I. (1967).Journal of Functional Analysis,1, 1.Google Scholar

Copyright information

© Plenum Publishing Company Limited 1969

Authors and Affiliations

  • P. Roman
    • 1
  • R. M. Santilli
    • 1
  1. 1.Department of PhysicsBoston UniversityBoston

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