Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Generalization of the Dirac equation admitting isospin and color symmetries

Abstract

One possible generalization of the Dirac “square root” procedure μ μ=D d k D d is presented, based on the explicit introduction of chiral symmetry, which generates a set {d} of symmetry-constrained Dirac fieldsD d ψ d =0admitting isospin and color. A self-consistent discussion is given of the basic geometrical construction, the field equations, and their relationship to chiral symmetry, isospin, and color, and of the construction of the Lagrangian, including the interaction gauge fields. The correspondence of the theory with the standardSU c(3) ×SU w(2) ×U y(1) formulation for quarks and leptons is shown.

This is a preview of subscription content, log in to check access.

References

  1. Boudet, R. (1971).Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences (Paris), Serie A,272, 767.

  2. Boudet, R. (1974).Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences (Paris), Serie A,278, 1063.

  3. Boudet, R. (1985).Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences (Paris), Serie, II 300, 157.

  4. Casanova, G. (1970).Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences (Paris), Serie A,270, 1202.

  5. Casanova, G. (1976).L'algebre vectorielle, Presses Universitaires de France, Paris.

  6. Close, F. E. (1979).An Introduction to Quark and Partons, Academic Press, London.

  7. Eddington, A. S. (1936).Relativity Theory of Protons and Electrons, Macmillan, New York, and references therein.

  8. Field, R. D. (1979).Quantum Flavordynamics, Quantum Chromodynamics and Unified Theories (NATO Advanced Study Series, Series B, Physics. Vol. 54), Plenum Press, New York.

  9. Fritzch, H., and Minkowski, P. (1974).Annals of Physics (New York),93, 193.

  10. Georgi, H. (1975). InParticles and Fields, C. E. Carlson, ed., American Institute of Physics, New York.

  11. Georgi, H., and Glashow, S. L. (1974).Physical Review Letters,32, 438.

  12. Greenberg, O. W. (1964).Physical Review Letters,13, 598.

  13. Greenberg, O. W. (1982).American Journal of Physics,50, 1074.

  14. Greider, T. K. (1980).Physical Review Letters,44, 1718.

  15. Halzen, F., and Martin A. D. (1984).Quarks and Leptons, Wiley, New York.

  16. Hestenes, D. (1966).Spacetime Algebra, Gordon and Breach, New York.

  17. Hestenes, D. (1975).Journal of Mathematical Physics,16, 556, and references therein.

  18. Hestenes, D., and Sobczyk, G. (1984).Clifford Algebra to Geometric Calculus, Reidel, Dordrecht.

  19. Huang, K. (1982).Leptons and Partons, Academic Press, London.

  20. Juvet, G. (1930).Commentarii Mathematici Helvetici,2, 225.

  21. Juvet, G. (1932).Bulletin de la Societé Neuchateloise des Sciences Naturelles,57, 127.

  22. Keller, J. (1981).Revista de la Sociedad Quimica de Mexico,25, 28.

  23. Keller, J. (1983a).International Journal of Theoretical Physics,21, 829.

  24. Keller, J. (1982)b). InProceedings of the Mathematics of the Physical Spacetime, Mexico 1982, J. Keller, ed., p. 117, University of Mexico.

  25. Keller, J. (1984).International Journal of Theoretical Physics,23, 818.

  26. Keller, J. (1985). InProceedings of the NATO & SERC Workshop on “Clifford Algebras and their Applications in Mathematical Physics” (Canterbury, 1985), J. S. R. Chisholm and A. K. Common, eds., Reidel, Dordrecht.

  27. Keller, J., Rodriguez, S., and Peña, A. (1986). In preparation.

  28. Marlow, A. R. (1982). InProceedings of the Mathematics of the Physical Spacetime, Mexico 1982, J. Keller, ed., p. 97, University of Mexico.

  29. Marlow, A. R. (1984).International journal of Theoretical Physics,23, 863.

  30. Mercier, A. (1934).Actes de la Societé Helvetique des Sciences Naturelles Zürich,1934, 278.

  31. Mercier, A. (1935). These, Université de Génève;Archives des Sciences Physiques et Naturelles (Suisse),17, 278.

  32. Okun, L. B. (1982).Leptons and Quarks, North-Holland, Amsterdam.

  33. Proca, A. (1930a).Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences (Paris),190, 1377.

  34. Proca, A. (1930b).Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences (Paris),191, 26.

  35. Proca, A. (19830).Journal de Physique, VII 1, 236.

  36. Quilichini, P. (1971).Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences (Paris), Serie B,273, 829.

  37. Ravsevskii, P. K. (1957).Transactions of the American Mathematical Society,6, 1.

  38. Riesz, M. (1946). In,Comptes Rendus du Dixieme Congres des Mathematiques des Pays Scandinaves, Vol. 123, Copenhagen.

  39. Riesz, M. (1953). InComptes Rendus du Douzieme Congres des Mathematiques des Pays Scandinaves, Vol. 241, Lund.

  40. Riesz, M. (1958). Lecture Series No. 38, University of Maryland.

  41. Salam, A. (1968). InProceedings 8th Nobel Symposium, N. Svartholm, ed., p. 367,Almquist and Wiksell, Stockholm

  42. Salingaros, N., and Dresden, M. (1979).Physical Review Letters,43.

  43. Sauter, F. (1930).Zeitschrift für Physik,63, 803;64, 295.

  44. Smith, F. (1985).International Journal of Theoretical Physics,24, 155.

  45. Sommerfeld, A. (1939).Atombau and Spektrallinien, Vol. II. p. 217, Braunschweig.

  46. Teitler, S. (1965a).Nuovo Cimenta Supplemento,3, 1.

  47. Teitler, S. (1965b).Nuovo Cimenta Supplemento,3, 15.

  48. Teitler, S. (1965c).Journal of Mathematical Physics,6, 1976.

  49. Teitler, S. (1966a).Journal of Mathematical Physics,7, 1730.

  50. Teitler, S. (1966b).Journal of Mathematical Physics,7, 1739.

  51. Weinberg, S. (1967).Physical Review Letters,19, 1264.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Keller, J. Generalization of the Dirac equation admitting isospin and color symmetries. Int J Theor Phys 25, 779–806 (1986). https://doi.org/10.1007/BF00669917

Download citation

Keywords

  • Color
  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Field Equation