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A comparative review of certain gauge theories of the gravitational field

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Abstract

A general formal analysis is made trying to obtain a better understanding and greater synthesis of the mathematical structure of the gravitational field's gauge theories. Under this approach, some misstatements appearing in current theories are detected. A theory based on the direct product groupsT(4)×GL(4) andT(4)×O(1, 3) is suggested (in contrast to those using the Poincaré group, semidirect product). Such a theory corrects the justmentioned deficiencies possessing the attributes of the preceding ones.

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References

  1. Utiyama, R. (1956).Phys. Rev.,101, 1597.

    Google Scholar 

  2. Kibble, T. W. B. (1961).J. Math. Phys.,2, 212.

    Google Scholar 

  3. Kerner, R. (1968).Ann. Inst. Henri Poincaré,IX, 143.

    Google Scholar 

  4. Cho, Y. M. (1975).J. Math. Phys.,16, 2029.

    Google Scholar 

  5. Cho, Y. M. (1976).Phys. Rev. D,14, 2521.

    Google Scholar 

  6. Cho, Y. M. (1976).Phys. Rev. D,14, 3335.

    Google Scholar 

  7. Cho, Y. M. (1976).Phys. Rev. D,14, 3341.

    Google Scholar 

  8. Chang, L. N., Macrae, K. I., and Mansouri, F. (1976).Phys. Rev. D,13, 235.

    Google Scholar 

  9. Mansouri, F., and Chang, L. N. (1976).Phys. Rev. D,13, 3192.

    Google Scholar 

  10. Trautman, A. (1970).Rep. Math. Phys.,1, 29.

    Google Scholar 

  11. Trautman, A. (1976).Rep. Math. Phys.,10, 297.

    Google Scholar 

  12. Lichnerowicz, A. (1971).Gen. Rel. Grav.,1, 235.

    Google Scholar 

  13. Kaluza, T. (1921).Sitzungsber. Preuss. Akad. Wiss., 966.

  14. Klein, O. (1926).Z. Phys.,37, 895.

    Google Scholar 

  15. Choquet-Bruhat, Y. (1968).Géométrie Différentielle et Systèmes Extérieurs (Dunod, Paris).

    Google Scholar 

  16. Kobayashi, S., and Nomizu, K. (1963).Foundations of Differential Geometry (Interscience New York).

    Google Scholar 

  17. Hayashi, K., and Nakano, T. (1961).Progr. Theor. Phys.,38, 491.

    Google Scholar 

  18. Yang, C. N. (1974).Phys. Rev. Lett.,33, 445.

    Google Scholar 

  19. Burghardt, R. (1973).Acta Phys. Austr.,38, 327.

    Google Scholar 

  20. Burghardt, R. (1974).Acta Phys. Austr.,39, 31.

    Google Scholar 

  21. Burghardt, R. (1974).Acta Phys. Austr.,39, 127.

    Google Scholar 

  22. Nascimento, J. C. (1977). Report PUC 13/77, Pont. Univ. Catol. Rio de Janeiro.

  23. Faischild, E. E., Jr., (1976).Phys. Rev. D,14, 384.

    Google Scholar 

  24. Stephenson, G. (1977).J. Phys. A. Math. Gen.,10, 181.

    Google Scholar 

  25. Pavelle, R. (1978).Phys. Rev. Lett.,40, 267.

    Google Scholar 

  26. Cartan, E. (1922).C. R. Acad. Sci. Paris,174, 593.

    Google Scholar 

  27. Cartan, E. (1923).Ann. Ec. Norm. Sup. (3),40, 325.

    Google Scholar 

  28. Cartan, E. (1924).Ann. Ec. Norm. Sup. (3),41, 1.

    Google Scholar 

  29. Trautman, A. (1972).Bull. Acad. Pol. Sci.,XX, 185.

    Google Scholar 

  30. Trautman, A. (1972).Bull. Acad. Pol. Sci.,XX, 503.

    Google Scholar 

  31. Hehl, F. W. (1973).Gen. Rel. Grav.,4, 333.

    Google Scholar 

  32. Hehl, F. W. (1974).Gen. Rel. Grav.,5, 491.

    Google Scholar 

  33. Camezind, M. (1975).J. Math. Phys.,16, 1023.

    Google Scholar 

  34. Camezind, M. (1977).Gen. Rel. Grav.,8, 103.

    Google Scholar 

  35. Lord, E. A. (1978).Phys. Lett.,65A, 1.

    Google Scholar 

  36. Hermann, R. (1979).Vector Bundles in Mathematical Physics (Benjamin, New York).

    Google Scholar 

  37. Drechsler, W., and Mayer, M. E. (1977).Fiber Bundle Techniques in Gauge Theory, Lecture Notes in Physics (Springer Verlag, Berlin).

    Google Scholar 

  38. de Rham, G. (1960).Variétés Differentiates (Hermann, Paris).

    Google Scholar 

  39. Domokos, G., and Kövesi Domokos, S. (1978).Nuovo Cimenta,44A, 318.

    Google Scholar 

  40. Harnad, J. P., and Pettitt, R. B. (1976).J. Math. Phys.,17, 1827.

    Google Scholar 

  41. von der Heyde, P. (1976).Phys. Lett.,58A, 141.

    Google Scholar 

  42. Cho, Y. M., and Freund, P. G. O. (1975).Phy. Rev. D,12, 1711.

    Google Scholar 

  43. Wu, T. T., and Yang, C. N. (1975).Phys. Rev. D,12, 3845.

    Google Scholar 

  44. Kaempffer, F. A. (1968).Phys. Rev.,165, 1420.

    Google Scholar 

  45. Sandverg, V. D. (1975).Phys. Rev. D,12, 3013.

    Google Scholar 

  46. Skinner, R., and Gregorash, D. (1916).Phys. Rev. D,14, 3314.

    Google Scholar 

  47. Nester, J. M. (1977).Phys. Rev. D,16, 2395.

    Google Scholar 

  48. Stephenson, G. (1958).Nuovo Cimento,9, 263.

    Google Scholar 

  49. Hamamoto, S. (1977).Progr. Theor. Phys.,58, 710.

    Google Scholar 

  50. Fairchild, E. E. (1977).Phys. Rev. D,16, 2438.

    Google Scholar 

  51. Carmeli, M. and Malin, S. (1977).Ann. of Phys.,103, 208.

    Google Scholar 

  52. Cho, Y. M., and Yang, P. S. (1915).Phys. Rev. D 12, 3789.

    Google Scholar 

  53. Agnese, A. G., and Calvini, P. (1975).Phys. Rev. D,12, 3800.

    Google Scholar 

  54. Agnese, A. G., and Calvini, P. (1975).Phys. Rev. D,12, 3804.

    Google Scholar 

  55. Toller, M. (1978).Nuovo Cimento,44B, 67.

    Google Scholar 

  56. Lubkin, E. (1963).Ann. of Phys.,23, 233.

    Google Scholar 

  57. Hehl, F. W., von der Heyde, P., Kerlick, G. D., and Nester, J. M. (1976).Rev. of Mod. Phys.,48, 393.

    Google Scholar 

  58. Brodskii, A. M., Ivanenko, D., and Sokolik, G. A. (1962).Sov. Phys. JEPT,14, 930.

    Google Scholar 

  59. Derbes, D. (1918).Nuovo Cimento,45B, 31.

    Google Scholar 

  60. Lichnerowicz, A. (1955).Théorie Globale des Connexions et des Groupes d'Holonomie (Edizioni Cremonese-Roma).

    Google Scholar 

  61. MacLane, S., and Birkhoff, G. (1967).Algebra (Macmillan, New York).

    Google Scholar 

  62. Sciama, D. W. (1962).

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Comisión Nacional de Energía Atómica.

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Basombrío, F.G. A comparative review of certain gauge theories of the gravitational field. Gen Relat Gravit 12, 109–136 (1980). https://doi.org/10.1007/BF00756467

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