Conclusion
The principal difficulty that has obstructed the formulation of gauge gravitation for more than twenty years now is the fact that an Einstein gravitational field represents a metric or a tetradic field, while gauge fields are connections on fiber bundles.
The popular approach to the resolution of this problem lies in attempts to represent tetrad fields as gauge fields of the translation subgroup within the framework of the gauge theory of the Poincaré group, but the existing set of variants of the latter theory indicate that it is a long way from completion.
Our approach [2, 3] insists that in a gauge theory, apart from gauge fields, the situation of spontaneous breaking of symmetry can also admit Goldstone and Higgs fields, under which is subsumed the metric (tetrad) gravitational field by virtue of the fact that, as we have shown above, the equivalence principle is included in the gauge theory of gravitation.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 79–82, June, 1981.
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Ivanenko, D., Sardanashvili, G. Relativity and equivalence principles in a gauge theory of gravitation. Soviet Physics Journal 24, 555–557 (1981). https://doi.org/10.1007/BF00892957
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DOI: https://doi.org/10.1007/BF00892957