General Relativity and Gravitation

, Volume 19, Issue 10, pp 983–1002 | Cite as

A unified approach to the gauging of space-time and internal symmetries

  • Eric A. Lord
Research Articles

Abstract

The properties of the manifold of a Lie groupG, fibered by the cosets of a sub-groupH, are exploited to obtain a geometrical description of gauge theories in space-timeG/H. Gauge potentials and matter fields are pullbacks of equivariant fields onG. Our concept of a connection is more restricted than that in the similar scheme of Ne'eman and Regge, so that its degrees of freedom are just those of a set of gauge potentials forG, onG/H, with no redundant components. The “translational” gauge potentials give rise in a natural way to a nonsingular tetrad onG/H. The underlying groupG to be gauged is the groupG of left translations on the manifoldG and is associated with a “trivial” connection, namely the Maurer-Cartan form. Gauge transformations are all those diffeomorphisms onG that preserve the fiber-bundle structure.

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References

  1. 1.
    Daniel, M., and Viallet, C. M. (1980).Rev. Mod. Phys.,52, 175.Google Scholar
  2. 2.
    Eguchi, T., Gilkey, P. B., and Hanson, A. J. (1980).Phys. Rep.,66, 213.Google Scholar
  3. 3.
    Ivanenko, D., and Sardanashvily, G. (1983).Phys. Rep.,94, 1.Google Scholar
  4. 4.
    Dass, T. (1984).Pramana,23, 433.Google Scholar
  5. 5.
    Kobayashi, S., and Nomizu, K. (1963).Foundations of Differential Geometry (Interscience, New York), Vol. 1.Google Scholar
  6. 6.
    Harnad, J. P., and Pettitt, R. B. (1977). InGroup Theoretical Methods in Physics, Proceedings of the V International Colloquium, Sharp, R. T., and Kolman, B., eds. (Academic Press, New York), 277.Google Scholar
  7. 7.
    Ne'eman, Y., and Regge, T. (1978).Riv. del Nuovo Cim.,1, no. 5.Google Scholar
  8. 8.
    Lord, E. A., and Goswami, P. (1986).J. Math. Phys.,27, 2415.Google Scholar
  9. 9.
    Atiyah, M. F., Hitchin, N. J., and Singer, I. M. (1978).Proc. Roy. Soc. A,362, 425.Google Scholar
  10. 10.
    Von der Heyde, P. (1978).Phys. Lett. A,58, 141.Google Scholar
  11. 11.
    Hehl, F. W. (1978). InProceedings of the 6th Course of the International School of Cosmology and Gravitation, Bergmann, P. G., and de Sabbata, V., eds. (Plenum Press, New York).Google Scholar
  12. 12.
    Pérez-Rendon, A., and Ruiperez, D. H. (1984). InDifferential Geometric Methods in Mathematical Physics, Sternberg, S., ed. (D. Reidel Publishing Co., New York).Google Scholar
  13. 13.
    Lord, E. A., and Goswami, P. (1985).Pramana,25, 635.Google Scholar
  14. 14.
    Coleman, S., Wess, J., and Zumino, B. (1969).Phys. Rev. D,12, 1711.Google Scholar
  15. 15.
    Salam, A., and Strathdee, J. (1969).Phys. Rev.,184, 1750.Google Scholar
  16. 16.
    Callan, C. G., Coleman, S., Wess, J., and Zumino, B. (1969).Phys. Rev. D,12, 2247.Google Scholar
  17. 17.
    Tseytlin, A. A. (1982).Phys. Rev. D,26, 3327.Google Scholar
  18. 18.
    Harnad, J. P., and Pettitt, R. B. (1976).J. Math. Phys.,17, 1827.Google Scholar
  19. 19.
    Thierry-Mieg, J. (1980).Nuovo Cim. A,56, 396.Google Scholar
  20. 20.
    Ne'eman, Y., Takasugi, E., and Thierry-Mieg, J. (1980).Phys. Rev. D,22, 2371.Google Scholar

Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • Eric A. Lord
    • 1
  1. 1.Department of Applied MathematicsIndian Institute of ScienceBahgaloreIndia

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