Gauge theory for the Poincaré group
- 41 Downloads
Theories containing the squares of the curvature and torsion tensors have recently been investigated from various points of view. Stelle  showed that a theory with Lagrangian of the type R(e)+R2(e) is renormalizable but not unitary. Sezgin and Van Nieuwenhuizen  found a general class of Lagrangians free of ghosts and tachyons. Rauch and Nieh  proved Brikhoff's theorem in a number of cases, and Fradkin and Tseitlin  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  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.
KeywordsGauge Theory Ghost Cosmological Constant General Class Curvature Tensor
Unable to display preview. Download preview PDF.
- 1.Y. M. Cho, J. Math. Phys.16, 2029 (1975).Google Scholar
- 2.R. Utiyama, Phys. Rev.,101, 1597 (1956).Google Scholar
- 3.F. W. Hehl, P. von der Heyde G. D. Kerlick, and J. M. Nester, Rev. Mod. Phys.,48, 393 (1976).Google Scholar
- 4.F. G. Basombrio, Gen. Rel. Grav.,12, 109 (1980).Google Scholar
- 5.K. Hayashi and T. Shirafuji, Prog. Theor. Phys.,64, 866 (1980).Google Scholar
- 6.S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. 1, Interscience Publishers, New York (1963), p. 307.Google Scholar
- 7.Y. M. Cho, Phys. Rev. D,14, 3335 (1976).Google Scholar
- 8.J. Hennig and J. Nitsch, Gen. Rel. Grav.,13, 947 (1981).Google Scholar
- 9.C. P. Luehr and M. P. Rosenbaum, J. Math. Phys.,21, 1432 (1980).Google Scholar
- 10.F. Mansouri and L. N. Chang, Phys. Rev. D,13, 3192 (1976).Google Scholar
- 11.K. S. Stelle, Phys. Rev. D,16, 953 (1977).Google Scholar
- 12.E. Sezgin and P. Van Nieuwenhuizen, Phys Rev. D,21, 3269 (1980).Google Scholar
- 13.R. Rauch and H. T. Nieh, Phys. Rev. D,24, 2029 (1981).Google Scholar
- 14.E. S. Fradkin and A. A. Tseytlin, Phys. Lett. B,110, 117 (1982).Google Scholar