Theoretical and Mathematical Physics

, Volume 54, Issue 3, pp 248–252 | Cite as

Gauge theory for the Poincaré group

  • M. O. Katanaev
Article

Conclusions

Theories containing the squares of the curvature and torsion tensors have recently been investigated from various points of view. Stelle [11] showed that a theory with Lagrangian of the type R(e)+R2(e) is renormalizable but not unitary. Sezgin and Van Nieuwenhuizen [12] found a general class of Lagrangians free of ghosts and tachyons. Rauch and Nieh [13] proved Brikhoff's theorem in a number of cases, and Fradkin and Tseitlin [14] proved the existence of asymptotic freedom in conformal supergravity, which also contains the square of the curvature tensor.

Our Lagrangian differs from the one considered in [11] by the presence of torsion and from [12, 13] by the presence of the cosmological constant. This makes it impossible to transfer the corresponding results to the Lagrangian (9) so that the questions of unitarity and renormalizability require further investigation.

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Literature Cited

  1. 1.
    Y. M. Cho, J. Math. Phys.16, 2029 (1975).Google Scholar
  2. 2.
    R. Utiyama, Phys. Rev.,101, 1597 (1956).Google Scholar
  3. 3.
    F. W. Hehl, P. von der Heyde G. D. Kerlick, and J. M. Nester, Rev. Mod. Phys.,48, 393 (1976).Google Scholar
  4. 4.
    F. G. Basombrio, Gen. Rel. Grav.,12, 109 (1980).Google Scholar
  5. 5.
    K. Hayashi and T. Shirafuji, Prog. Theor. Phys.,64, 866 (1980).Google Scholar
  6. 6.
    S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. 1, Interscience Publishers, New York (1963), p. 307.Google Scholar
  7. 7.
    Y. M. Cho, Phys. Rev. D,14, 3335 (1976).Google Scholar
  8. 8.
    J. Hennig and J. Nitsch, Gen. Rel. Grav.,13, 947 (1981).Google Scholar
  9. 9.
    C. P. Luehr and M. P. Rosenbaum, J. Math. Phys.,21, 1432 (1980).Google Scholar
  10. 10.
    F. Mansouri and L. N. Chang, Phys. Rev. D,13, 3192 (1976).Google Scholar
  11. 11.
    K. S. Stelle, Phys. Rev. D,16, 953 (1977).Google Scholar
  12. 12.
    E. Sezgin and P. Van Nieuwenhuizen, Phys Rev. D,21, 3269 (1980).Google Scholar
  13. 13.
    R. Rauch and H. T. Nieh, Phys. Rev. D,24, 2029 (1981).Google Scholar
  14. 14.
    E. S. Fradkin and A. A. Tseytlin, Phys. Lett. B,110, 117 (1982).Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • M. O. Katanaev

There are no affiliations available

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