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Prog. Theor. Phys. Vol. 34 No. 6 (1965) pp. 1023-1039

[ Full Text PDF : FREE ACCESS (963K) ]

An Extension of Inversion with a Non-Abelian Group of Parity Tripod

Takao Okabayashi

Department of Physics, University of Tokyo, Tokyo

(Received August 14, 1965)

Abstract:

An extension of inversion (and therefore of the full group of inhomogeneous Lorentz transformations) with a non-Abelian group, group of parity tripod, is proposed (§2). It gives a foundation of the equation which was proposed by the present author several years ago (§3), and a correlation of the selection rule about hypercharge with the violation of the conservation law of parity. The expectation values of the two generators of the group of parity tripod are identified with hypercharge and K-mesonic charge. The empirical formulae for the strong interactions of pions and kaons and for the weak interactions of pions are tentatively expressed by the direct product group of the extended group with the isotopic spin group in the doublet description of baryons (§4). The results are very suggestive to seek the intimate connection of the group of parity tripod with the isotopic spin group, although they cannot have the final forms.


URL : http://ptp.ipap.jp/link?PTP/34/1023/
DOI : 10.1143/PTP.34.1023

[ Full Text PDF : FREE ACCESS (963K) ] Citation:

References:

  1. T. Okabayashi, Prog. Theor. Phys. 20 (1958), 583[PTP].
    This article will be cited as I hereafter.
  2. T. Okabayashi, Prog. Theor. Phys. 21 (1959), 867[PTP].
  3. T. Okabayashi, Prog. Theor. Phys. 21 (1959), 653[PTP].
    T. Okabayashi, Nuovo Cim. 32 (1964), 619.
  4. T. Okabayashi, S. Nakamura and Y. Nishiyama, Prog. Theor. Phys. 25 (1961), 701[PTP].
  5. T. Okabayashi, I. Hamamoto, A. Hatano and T. Saikan, Prog. Theor. Phys. 29 (1963), 767 [PTP][Errata; 30 (1963), 412[PTP]].
  6. T. Okabayashi, Prog. Theor. Phys. 30 (1963), 96[PTP].
  7. Tripp et al., Phys. Rev. Lett. 9 (1962), 66[APS].
    Leitner et al., Phys. Rev. Lett. 7 (1961), 264[APS].
    Eisler et al., Phys. Rev. 108 (1958), 1353[APS].
    Carmony et al., Phys. Rev. Lett. 12 (1964), 482[APS].
  8. M. Kato and G. Takeda, Prog. Theor. Phys. Suppl. No. 7 (1959), 35[PTP].
  9. M. Gell-Mann, Phys. Rev. 92 (1953), 833[APS].
    T. Nakano and K. Nishijima, Prog. Theor. Phys. 10 (1953), 581[PTP].
    K. Nishijima, Prog. Theor. Phys. 12 (1954), 107[PTP]; ibid. 13 (1955), 285[PTP].
  10. T. D. Lee and C. N. Yang, Phys. Rev. 102 (1956), 290[APS].
    Wu et al., Phys. Rev. 105 (1957), 1413[APS].
    Garwin et al., Phys. Rev. 105 (1957), 1415[APS].
  11. M. Kato and G. Takeda, Prog. Theor. Phys. 21 (1959), 411[PTP].
  12. Th. Kaluza, S. B. preuss Akad. Wiss. (1921), 966.
    O. Klein, Z. Physik 37 (1926), 895; ibid. 46 (1927), 188.
    B. Hoffmann, Quaterly J. Math. 7 (1936), 20.
    A. Einstein and W. Mayer, S. B. preuss Akad. Wiss. (1931), 541; ibid. (1932), 130.
    B. Hoffmann, Quaterly J. Math. 7 (1936), 32.
    P. A. M. Dirac, Ann. of Math. 36 (1935), 657.
    P. A. M. Dirac, Ann. of Math. 37 (1936), 429.
  13. H. Zassenhaus, The Theory of Groups (Chelsea, New York, 1956), 124.
    L. Michel, Lectures on the theory of group extensions at the Istanbul Summer School on Theoretical Physics (Gordon and Breach, New York, 1962), 135.
  14. K. Nakagawa, Nucl. Phys. 10 (1959), 20[CrossRef].
  15. M. Gell-Mann, Phys. Rev. 106 (1957), 1296[APS].
  16. A. Pais, Phys. Rev. 110 (1958), 574[APS]; ibid. 110 (1958), 1480[APS].
  17. J. J. Sakurai, Phys. Rev. 113 (1959), 1679[APS].
  18. E. Cartan, Leçons sur la theorie des spineurs (Hermann, Paris, 1938).
  19. T. Okabayashi, Soryushiron kenkyu (mimeographed circular in Japanese) 21 (1960), 523; ibid. 22 (1961), 564.
    T. Okabayashi, Reports of Research Group on Mathematical Science (1960) No. 1-6, p. 4.
  20. T. Okabayashi, Prog. Theor. Phys. 10 (1953), 499[PTP].
    T. Okabayashi, Nuovo Cim. Suppl. 9 (1958), 599.
  21. M. Ikeda, S. Ogawa and Y. Ohnuki, Prog. Theor. Phys. 22 (1959), 715[PTP]; ibid. 23 (1960), 1073[PTP]; ibid. 25 (1961), 1[PTP].
    M. Gell-Mann, Phys. Rev. 125 (1961), 1067[APS].
    Y. Ne'eman, Nucl. Phys. 26 (1961), 222[CrossRef].
  22. F. Gürsey and L. A. Radicati, Phys. Rev. Lett. 13 (1964), 173[APS].
    F. Gürsey, A. Pais and L. A. Radicati, Phys. Rev. Lett. 13 (1964), 301[APS].
    B. Sakita, Phys. Rev. 136 (1964), B 1756[APS].
  23. S. Okubo, Prog. Theor. Phys. 27 (1962), 949[PTP].
    S. P. Rosen, Phys. Rev. Lett. 11 (1963), 100[APS].
  24. Barnes et al., Phys. Rev. Lett. 12 (1964), 204[APS].
    Barnes et al., Phys. Lett. 12 (1964), 134[CrossRef].
    Glasser et al., Phys. Rev. Lett. 13 (1964), 670[APS].
  25. Christenson et al., Phys. Rev. Lett. 13 (1964), 138[APS].
    Anderson et al., Phys. Rev. Lett. 14 (1965), 475[APS].
  26. Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122 (1961), 345[APS].
    T. Okabayashi, K. Tanabe and M. Yamada, Prog. Theor. Phys. 32 (1964), 619[PTP].
  27. E. J. Konopinski and H. M. Mahmoud, Phys. Rev. 92 (1953), 1045[APS].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 35 No. 5 (1966) pp. 840-857 :
    Broken Symmetry and the Stability of Particle-like States
    Takao Okabayashi and Seiichi Naitô

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