paper

On the choice of coupling procedure for the Poincaré gauge theory of gravity

arXiv:0902.4432 · doi:10.1103/PhysRevD.79.127501

Abstract

The gauge approach to the theory of gravity has been widely discussed as an alternative to standard general relativity. The Poincar{é} group, as a symmetry group of all relativistic theories in the absence of gravitation, constitutes the most natural candidate for a gauge group. Although the Poincar{é} gauge theory of gravity has been elaborated over the years and cast into a beautiful formal framework, some fundamental problems have remained unsolved. One of them concerns the inclusion of matter. The minimal coupling procedure, which is employed in standard Yang--Mills theories, appears to be ambiguous in the case of gravity. We propose a slight modification of this procedure, which removes the ambiguity. Our modification justifies some earlier results concerning the consequences of the Poincar{é} gauge theory of gravity. In particular, the predictions of Einstein--Cartan theory with fermionic matter are rendered unique. We recall the earlier proposed solution based on modified volume--forms. The advantage of our modification is that the predictions of the theory are not radically changed. Basically, this modification simply justifies the results that were obtained partly `by chance' in the hitherto prevailing accounts on the Einstein--Cartan theory. The only difference in the predictions, when compared to the standard treatment, concerns the Proca field in the presence of gravity. The `torsion singularities' which occur there are shifted towards other values of the field.

15 pages, linguistic corrections

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