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Prog. Theor. Phys. Vol. 64 No. 4 (1980) pp. 1435-1452

[ Full Text PDF : FREE ACCESS (1083K) ]

Gravity from Poincaré Gauge Theory of the Fundamental Particles. III

— Weak Field Approximation —

Kenji Hayashi and Takeshi Shirafuji*

Institute of Physics, University of Tokyo, Tokyo 153
*Physics Department, Saitama University, Urawa 338

(Received May 17, 1980)

Abstract:

We apply the weak field approximation to the most general gravitational field equations in Poincaré gauge theory. The weak gravitational field hµν is a multimass field obeying a fourth-order field equation. In the Newtonian approximation we show that there are two routes to arrive at the Newtonian potential. The torsion field is decomposed into six irreducibe building blocks with spinparity, 2+, 2-, 1+, 1-, 0+ and 0-, each of which obeys the Klein-Gordon equation. Finally, we construct a possible candidate for the massless graviton field which obeys the linearized Einstein equation.


URL : http://ptp.ipap.jp/link?PTP/64/1435/
DOI : 10.1143/PTP.64.1435

[ Full Text PDF : FREE ACCESS (1083K) ] Citation:

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References:

  1. K. Hayashi and T. Shirafuji, Prog. Theor. Phys. 64 (1980), 866[PTP].
    These papers are called here I and II, respectively.
  2. K. Hayashi and T. Shirafuji, Phys. Rev. D 19 (1979), 3524[APS].
  3. R. Bach, Math. Z. 9 (1921), 110.
    C. Lanczos, Ann. of Math. 39 (1938), 842.
  4. F. W. Hehl, Y. Ne'eman, J. Nitsch and P. von der Heyde, Phys. Lett. B 78 (1978), 102[CrossRef].
    F. W. Hehl, J. Nitsch and P. von der Heyde, in the Einstein Commemorative Volume, ed. A. Held (Plenum Press, New York, 1980), p. 329.
  5. Y. Ne'eman, preprint TUAP 763-79.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 64 No. 6 (1980) pp. 2222-2241 :
    Gravity from Poincaré Gauge Theory of the Fundamental Particles. IV
    Kenji Hayashi and Takeshi Shirafuji
  2. Progress of Theoretical Physics Vol. 65 No. 2 (1981) pp. 525-532 :
    Gravity from Poincaré Gauge Theory of the Fundamental Particles. V
    Kenji Hayashi and Takeshi Shirafuji
  3. Progress of Theoretical Physics Vol. 66 No. 1 (1981) pp. 287-302 :
    On Supergravity with Propagating Lorentz Connexion
    Hitoshi Nishino
  4. Progress of Theoretical Physics Vol. 66 No. 1 (1981) pp. 318-336 :
    Gravity from Poincaré Gauge Theory of the Fundamental Particles. VI
    Kenji Hayashi and Takeshi Shirafuji
  5. 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
  6. Progress of Theoretical Physics Vol. 66 No. 6 (1981) pp. 2011-2024 :
    Conformal and Axial Anomalies in Riemann-Cartan Space
    Toshiei Kimura
  7. Progress of Theoretical Physics Vol. 66 No. 6 (1981) pp. 2258-2273 :
    Gravity from Poincaré Gauge Theory of the Fundamental Particles. VII
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  8. Progress of Theoretical Physics Vol. 67 No. 3 (1982) pp. 990-992 :
    Constraints to Freeze Non-Propagating Modes of Lorentz Connexion
    Hitoshi Nishino
  9. Progress of Theoretical Physics Vol. 68 No. 3 (1982) pp. 975-988 :
    Local Tensor Calculus in Supergravity with Propagating Lorentz Connexion
    Hitoshi Nishino
  10. Progress of Theoretical Physics Vol. 68 No. 5 (1982) pp. 1765-1775 :
    Consistency of Couplings in Supergravity Theory with Propagating Lorentz Connexion
    Hitoshi Nishino
  11. 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
  12. 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
  13. Progress of Theoretical Physics Vol. 70 No. 2 (1983) pp. 622-624 :
    Torsion Coupling Constant of New General Relativity
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  14. Progress of Theoretical Physics Vol. 71 No. 1 (1984) pp. 183-200 :
    Dirac Equation on the Schouten Spacetime
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  15. Progress of Theoretical Physics Vol. 71 No. 3 (1984) pp. 633-647 :
    Massless Torsion Fields. I
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  16. Progress of Theoretical Physics Vol. 72 No. 1 (1984) pp. 83-97 :
    New Equation and Energy-Tensor of a Gravitational Field
    Ryoyu Utiyama
  17. Progress of Theoretical Physics Vol. 73 No. 1 (1985) pp. 54-74 :
    Energy, Momentum and Angular Momentum in Poincaré Gauge Theory
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  18. Progress of Theoretical Physics Vol. 73 No. 1 (1985) pp. 75-83 :
    Massless Torsion Fields. II
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  19. Progress of Theoretical Physics Vol. 73 No. 1 (1985) pp. 84-99 :
    Roles of Torsion Particles in the Very Early Universe
    Shinsuke Ogino
  20. 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
  21. Progress of Theoretical Physics Vol. 74 No. 4 (1985) pp. 852-865 :
    Conformal Rescalings Applied to Poincaré Gauge Theory
    Masayasu Fukui, Kenji Hayashi and Takeshi Shirafuji
  22. 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
  23. Progress of Theoretical Physics Vol. 79 No. 1 (1988) pp. 77-85 :
    Asymptotically Newtonian Conditions for Poincaré Gauge Theory
    Hui-Hua Chen, De-Ching Chern, Rue-Ron Hsu, James M. Nester and Wai Bong Yeung
  24. 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
  25. Progress of Theoretical Physics Vol. 79 No. 6 (1988) pp. 1420-1430 :
    Special Relativistic Limits of \overlinePoincaré Gauge Theory of Gravity
    Tetsuo Fukui, Toshiharu Kawai and Hirofumi Saitoh
  26. Progress of Theoretical Physics Vol. 81 No. 2 (1989) pp. 523-540 :
    A Spinor Approach to Poincaré Gauge Theory
    Shin-ichi Nakariki
  27. Progress of Theoretical Physics Vol. 82 No. 1 (1989) pp. 183-206 :
    Energy-Momentum and Angular Momentum in \overlinePoincaré Gauge Theory of Gravity and Physical Multiplets of Torsion Fields
    Tetsuo Fukui
  28. Progress of Theoretical Physics Vol. 82 No. 4 (1989) pp. 723-736 :
    Stability of the Friedmann Universe in the Poincaré Gauge Theory
    Shinsuke Ogino
  29. Progress of Theoretical Physics Vol. 84 No. 6 (1990) pp. 1074-1084 :
    Frame-Dragging Precession of Orbiting Gyroscopes in New General Relativity and Possible Violation of Equivalence Principle
    Kenji Hayashi and Takeshi Shirafuji
  30. Progress of Theoretical Physics Vol. 84 No. 6 (1990) pp. 1085-1099 :
    Spin Precession in Spacetime with Torsion
    Kenji Hayashi, Koichi Nomura and Takeshi Shirafuji
  31. Progress of Theoretical Physics Vol. 89 No. 2 (1993) pp. 371-388 :
    Stability of the Friedmann Universe in the Poincaré Gauge Theory. II
    Shinsuke Ogino
  32. Progress of Theoretical Physics Vol. 99 No. 6 (1998) pp. 971-992 :
    Schwarzschild Space-Time in Gauge Theories of Gravity
    Toshiharu Kawai, Eisaku Sakane and Takashi Tojo
  33. 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
  34. 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

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