HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 38 (1967) > Number 4
| Next Article >

Prog. Theor. Phys. Vol. 38 No. 4 (1967) pp. 966-986

[ Full Text PDF : FREE ACCESS (1077K) ]

Wave Equation with Mass and Spin Spectrum Based on O(3,3) Group for Relativistic Deformable Model

Takehiko Takabayasi

Department of Physics, Nagoya University, Nagoya

(Received May 24, 1967)

Abstract:

On the basis of the fact that the group SL(4,R) of relativistic linear deformation and rotation is isomorphic to SO(3,3), new transformation properties under the physical Lorentz transformation is assigned to the internal coordinate in the bilocal-type model, which is adopted as a simple relativistic example having internal movement. The new viewpoint leads to both integer and half-integer spin states and also to the first order wave equation, which contains a mass spectrum corresponding to infinite-dimensional representations of the inner Lorentz group.
On the other hand several versions of bilocal model which belong to the conventional identification of inner Lorentz group and represent oscillator or rotator type internal motion are successively discussed in the Appendix.


URL : http://ptp.ipap.jp/link?PTP/38/966/
DOI : 10.1143/PTP.38.966

[ Full Text PDF : FREE ACCESS (1077K) ] Citation:

References:

  1. T. Takabayasi, Internal Motion of Hadrons and Unified Model, NUDP-Report T-13 (1965).
  2. P. Budini and C. Fronsdal, Phys. Rev. Lett. 14 (1965), 968[APS].
  3. a) Y. Nambu, Infinite Component Wave Equations, preprint.
    b) A. O. Barut and H. Kleinert, preprint.
  4. E. Majorana, Nuovo Cim. 9 (1932), 335.
  5. H. Yukawa, Phys. Rev. 77 (1950), 219[APS]; ibid. 80 (1950), 1047[APS].
  6. T. Takabayasi, Prog. Theor. Phys. 37 (1967), 765[PTP]; ibid. 37 (1967), 767[PTP].
  7. H. Yukawa, Phys. Rev. 91 (1953), 415[APS]; ibid. 91 (1953), 416[APS].
  8. T. Takabayasi, Prog. Theor. Phys. Suppl. Extra Number (1965), 339[PTP].
  9. T. Takabayasi (and H. Kase), Prog. Theor. Phys. 36 (1966), 185[PTP]; ibid. 36 (1966), 187[PTP]; ibid. 36 (1966), 660[PTP]; ibid. 36 (1966), 662[PTP].
  10. Y. Nambu, Prog. Theor. Phys. Suppl. Nos. 37 & 38 (1966), 368[PTP].
  11. T. Takabayasi, Prog. Theor. Phys. 34 (1965), 124[PTP]; Nuovo Cim. 33 (1964), 668.
  12. G. Cocho, C. Fronsdal, I. T. Grodsky and R. White, Relativistic Harmonic Oscillator and Superconvergent Amplitudes, preprint.
  13. cf. S. Helgason, Differential Geometry and Symmetry Spaces.
  14. Y. Katayama, E. Yamada and H. Yukawa, Prog. Theor. Phys. 33 (1965), 541[PTP].
  15. O. Hara and T. Goto, Prog. Theor. Phys. Suppl. Extra Number (1965), 193[PTP].
  16. We add the following papers:
    O. Hara, T. Marumori, Y. Ohnuki and H. Shimodaira, Prog. Theor. Phys. 12 (1954), 177[PTP].
    M. Markov, Nuovo Cim. Suppl. 3 (1956), 760.
    V. L. Ginzburg, Acta Phys. Pol. 15 (1956), 163.
  17. I. M. Gel'fand, R. A. Minlos and Z. Y. Shipiro, Representations of the rotation and Lorentz groups and their applications (English translation, 1963).
  18. T. Takabayasi, Phys. Rev. 139 (1965), B1381[APS].
  19. C. Fronsdal, Infinite Multiplets and Hydrogen Atom, preprint.
  20. H. Yukawa, Prog. Theor. Phys. 31 (1964), 1167[PTP].
  21. V. Bargmann, Ann. of Math. 48 (1947), 568.
  22. E. P. Wigner, Theoretical Physics (IAEA, Vienna, 1963) p. 59.
  23. T. Takabayasi, Prog. Theor. Phys. 38 (1967), 285[PTP]; ibid. 38 (1967), 287[PTP].
  24. cf. P.A.M. Dirac, Quantum Mechanics, Second Edition.
  25. Trilocal model has been taken up occasionally: H. S. Green, Proceedings of the International Conference on Elementary Particles, Kyoto 1965, p. 159;
    Y. Katayama, Prog. Theor. Phys. 32 (1964), 368[PTP].
  26. The U(3,1) group was considered from different points of view also in B. Kursunoglu, Phys. Rev. 135 (1964), B761[APS];
    A. O. Barut, Nuovo Cim. 32 (1964), 234.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 39 No. 4 (1968) pp. 1047-1068 :
    Green's Function of Bilocal Field Equations
    Takeshi Shirafuji
  2. Progress of Theoretical Physics Vol. 42 No. 1 (1969) pp. 121-124 :
    Composite Particles with the Regge Mass Spectrum
    Tadashi Watanabe and Tadashi Miyazaki
  3. Progress of Theoretical Physics Vol. 42 No. 5 (1969) pp. 1210-1212 :
    Dynamical Group of Relativistic Oscillator and Linear Meson Trajectories
    Takehiko Takabayasi
  4. Progress of Theoretical Physics Vol. 44 No. 3 (1970) pp. 796-800 :
    Infinitely-Degenerate Particles and Mechanism of Mass Splitting
    Tadashi Miyazaki
  5. Progress of Theoretical Physics Vol. 45 No. 1 (1971) pp. 277-294 :
    A New Viewpoint on the Space-Time Model of Elementary Particles. I
    Said Heskia
  6. Progress of Theoretical Physics Vol. 45 No. 3 (1971) pp. 938-948 :
    Infinite Component Fields and Regge Amplitude
    Yasuo Matsumoto
  7. Progress of Theoretical Physics Vol. 47 No. 4 (1972) pp. 1385-1395 :
    How to Construct Wave Equations When Mass Levels Are Known?
    Tadashi Miyazaki
  8. Progress of Theoretical Physics Vol. 48 No. 5 (1972) pp. 1718-1741 :
    Bilocal Wave Equation for Baryons Lying on Linear Trajectories and Its Extension to a Linear Chain Model
    Takehiko Takabayasi
  9. Progress of Theoretical Physics Vol. 54 No. 2 (1975) pp. 563-577 :
    Relativistic Mechanics of Two Interacting Particles and Bilocal Theory
    Takehiko Takabayasi
  10. Progress of Theoretical Physics Vol. 57 No. 6 (1977) pp. 2127-2143 :
    Relativistic Mechanics of Interacting Particles and Multi-Local Theory. I
    Takehiko Takabayasi and Seiji Kojima
  11. Progress of Theoretical Physics Vol. 59 No. 6 (1978) pp. 2133-2148 :
    Constraints, Center-of-Masses and Quantization for Relativistically Structured Systems
    Takehiko Takabayasi and Kenji Takeuchi
  12. Progress of Theoretical Physics Vol. 60 No. 2 (1978) pp. 595-610 :
    Constituent Mass, Free-Limit Condition, and Quantization for Trilocal Theory
    Takehiko Takabayasi
  13. Progress of Theoretical Physics Vol. 61 No. 4 (1979) pp. 1235-1250 :
    Covariant Wave Equations of Two Spinning Particles Harmonically Bound
    Takehiko Takabayasi
  14. Progress of Theoretical Physics Supplement No.67 (1979) pp. 1-68 :
    Relativistic Mechanics of Confined Particles as Extended Model of Hadrons
    Takehiko Takabayasi

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.