HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 39 (1968) > Number 2
| Next Article >

Prog. Theor. Phys. Vol. 39 No. 2 (1968) pp. 494-515

[ Full Text PDF : FREE ACCESS (1252K) ]

Gauge Theories of Masive and Massless Tensor Fields

Kenji Hayashi

Department of Physics, Kyoto University, Kyoto

(Received October 4, 1967)

Abstract:

Extension of the Poincaré group is performed by replacing its ten constnat parameters by ten arbitrary functions. (For the purpose of comparison, similar procedures to extend a direct product of translation and internal symmetry groups are also carried out). Two independent sets of gauge fields are introduced corresponding to the group structure of semi-direct product of the translation and Lorentz groups. It is an essentially new result that the gauge fields associated with the Lorentz group can be massive only when free Lagrangians for both sets of gauge fields are considered simultaneously. It is shown that there are two solutions to satisfy the requirement that there should be no mass terms in resultant equations. A choice adopted in this paper is to impose field-field identity, viz. to represent the gauge fields of the Lorentz group in terms of the field strengths associated with the translation group; thus we obtain a set of equations to govern gravitation and further symmetrized energy-momentum tensors as its sources. All arbitrary coefficients (except for a cosmological constant) in free Lagrangians are determined by means of linear approximation. With a reasonable identification between the gauge fields and the metric tensors, the ensuing equations are shown to be equivalent to Einstein's equation of gravitation.


URL : http://ptp.ipap.jp/link?PTP/39/494/
DOI : 10.1143/PTP.39.494

[ Full Text PDF : FREE ACCESS (1252K) ] Citation:

References:

  1. For example, C. N. Yang and R. L. Mills, Phys. Rev. 96 (1954), 191[APS].
  2. See, for example, Kōdi Husimi, Lecture on Variational Principle in Field Theory in 1943 at the Meeting of Science Council of Japan (edited by the Japan Ministry of Education, 1944). Earlier references are listed in detail therein.
  3. R. Utiyama, Phys. Rev. 101 (1956), 1597[APS].
    M. Gell-Mann and S. Glashow, Ann. of Phys. 15 (1961), 437[CrossRef].
  4. T. W. B. Kibble, J. Math. Phys. 2 (1961), 212[CrossRef].
  5. K. Hayashi and T. Nakano, Prog. Theor. Phys. 38 (1967), 491[PTP].
  6. For example, L. S. Pontrijagin, Topological Group (Princeton University Press, Princeton, 1958).
  7. E. Cartan, Sur la Structure des Groupes de Transformations Finis et Continus, (1894; 2nd ed., 1933).
  8. For instance, A. O. Barut and R. Raczka, Proc. R. Soc. A 287 (1965), 519; earlier references are listed therein.
  9. M. Gell-Mann, CTSL-20 (1961).
  10. Y. Ne'man, Nucl. Phys. 26 (1961), 222[CrossRef].
  11. R. E. Behrends, J. Dreitlein, C. Fronsdal and B. W. Lee, Rev. Mod. Phys. 34 (1962), 1[APS].
  12. For the Young symmetrizer, see H. Weyl, The Classical Groups, Their Invariants and Representations (2nd ed., Princeton University Press, 1946).

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 41 No. 1 (1969) pp. 214-232 :
    High Spin Propagation of Massive and Massless Particles
    Kenji Hayashi
  2. Progress of Theoretical Physics Vol. 45 No. 1 (1971) pp. 295-311 :
    Possible Observation of the Skew-Symmetric Tensor Gauge Field
    Shikao Miyamoto and Tadao Nakano
  3. Progress of Theoretical Physics Vol. 49 No. 2 (1973) pp. 667-692 :
    Weyl Transformations and Poincaré Gauge Invariance
    Alexander Bregman
  4. Progress of Theoretical Physics Vol. 57 No. 5 (1977) pp. 1771-1780 :
    De Sitter Gauge Transformations of Dirac Equation
    P. K. Smrz
  5. Progress of Theoretical Physics Vol. 58 No. 2 (1977) pp. 710-712 :
    Poincaré Gauge Theory with Weyl-Type Lagrangian and Gravitation
    Shinji Hamamoto
  6. Progress of Theoretical Physics Vol. 59 No. 6 (1978) pp. 2080-2095 :
    Conversion of Isospin Degree of Freedom into Spin Degree of Freedom
    Masataka Hosoda and Hiroshi Kozakai
  7. Progress of Theoretical Physics Vol. 61 No. 1 (1979) pp. 326-333 :
    Nonlinear Realization of General Covariance Group
    Shinji Hamamoto
  8. Progress of Theoretical Physics Vol. 62 No. 1 (1979) pp. 266-277 :
    De Sitter Gauge Theory of Gravitation
    Toshiharu Kawai and Hideo Yoshida
  9. Progress of Theoretical Physics Vol. 62 No. 3 (1979) pp. 793-801 :
    Special Relativistic Limit of Gauge Theory of Gravitation
    Toshiharu Kawai and Hideo Yoshida
  10. Progress of Theoretical Physics Vol. 64 No. 3 (1980) pp. 866-882 :
    Gravity from Poincaré Gauge Theory of the Fundamental Particles. I
    Kenji Hayashi and Takeshi Shirafuji
  11. Progress of Theoretical Physics Vol. 64 No. 5 (1980) pp. 1596-1607 :
    De Sitter Gauge Theory of Gravitation. II
    Toshiharu Kawai and Hideo Yoshida
  12. Progress of Theoretical Physics Vol. 66 No. 2 (1981) pp. 481-497 :
    Linear Approximation for the Lorentz Gauge Field
    Shikao Miyamoto, Tadao Nakano, Teruya Ohtani and Yoshinobu Tamura
  13. Progress of Theoretical Physics Vol. 69 No. 4 (1983) pp. 1236-1240 :
    Linear Approximation for the Massless Lorentz Gauge Field
    Shikao Miyamoto, Tadao Nakano, Teruya Ohtani and Yoshinobu Tamura
  14. Progress of Theoretical Physics Vol. 69 No. 4 (1983) pp. 1272-1290 :
    A Five Dimensional Unification of the Poincaré Gauge and Electromagnetic Fields
    Toshiharu Kawai
  15. Progress of Theoretical Physics Vol. 70 No. 6 (1983) pp. 1648-1665 :
    Quaternionic Formulation of Dirac Theory in Special and General Relativity
    Katsusada Morita
  16. Progress of Theoretical Physics Vol. 72 No. 5 (1984) pp. 1056-1059 :
    Quaternions and Simple D=4 Supergravity
    Katsusada Morita
  17. Progress of Theoretical Physics Vol. 73 No. 1 (1985) pp. 54-74 :
    Energy, Momentum and Angular Momentum in Poincaré Gauge Theory
    Kenji Hayashi and Takeshi Shirafuji
  18. Progress of Theoretical Physics Vol. 73 No. 4 (1985) pp. 874-883 :
    Massless Lorentz Gauge Field Consistent with Einstein's Gravitation Theory
    Kazumi Fukuma, Shikao Miyamoto, Tadao Nakano, Teruya Ohtani and Yoshinobu Tamura
  19. Progress of Theoretical Physics Vol. 73 No. 4 (1985) pp. 999-1015 :
    Quaternionic Variational Formalism for Poincaré Gauge Theory and Supergravity
    Katsusada Morita
  20. Progress of Theoretical Physics Vol. 78 No. 1 (1987) pp. 16-21 :
    Mass and Spin of Exact Solutions of the Poincaré Gauge Theory
    Peter Baeckler, Ralf Hecht, Friedrich W. Hehl and Takeshi Shirafuji
  21. Progress of Theoretical Physics Vol. 78 No. 6 (1987) pp. 1470-1486 :
    Level Shift of Hyperfine Structure Due to the Lorentz Gauge Field
    Tetsuo Fukui, Kazumi Fukuma, Shikao Miyamoto, Tadao Nakano, Teruya Ohtani and Yoshinobu Tamura
  22. Progress of Theoretical Physics Vol. 79 No. 4 (1988) pp. 920-935 :
    Energy-Momentum and Angular Momentum in \overlinePoincaré Gauge Theory of Gravity
    Toshiharu Kawai
  23. Progress of Theoretical Physics Vol. 80 No. 4 (1988) pp. 711-730 :
    Gauge Theory of Gravitation
    Takeshi Shirafuji and Masahumi Suzuki
  24. Progress of Theoretical Physics Vol. 81 No. 2 (1989) pp. 523-540 :
    A Spinor Approach to Poincaré Gauge Theory
    Shin-ichi Nakariki
  25. Progress of Theoretical Physics Vol. 89 No. 5 (1993) pp. 1063-1075 :
    Internal P4cI Group in Spin Space and Gauge Theory of Gravity
    Hiroyuki Kikukawa, Junko Kikukawa and Akihiro Nakamura
  26. Progress of Theoretical Physics Vol. 97 No. 1 (1997) pp. 129-140 :
    Torsion Field Equation and Spinor Source
    Hong-Jun Xie and Takeshi Shirafuji
  27. Progress of Theoretical Physics Vol. 100 No. 1 (1998) pp. 179-190 :
    Interaction of Massless Dirac Field with a Poincaré Gauge Field
    Shin-ichi Nakariki, Takayuki Masaki, Kazumi Fukuma, Tetsuo Fukui, Masayoshi Mizouchi, Teruya Ohtani and Tsutomu Tashiro
  28. Progress of Theoretical Physics Vol. 107 No. 1 (2002) pp. 191-210 :
    Massless Modes of Lorentz Gauge Fields in Poincaré Gauge Theory of Gravity
    Kazumi Fukuma
  29. Progress of Theoretical Physics Supplement No.86 (1986) pp. 297-303 :
    Lorentz Gauge Field and Spin Angular-Momentum
    Tadao Nakano and Teruya Ohtani

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

Copyright © Progress of Theoretical Physics 2013 All rights reserved.