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The minimal coupling method proved to yield definite and correct physical predictions when applied to fundamental fermions within the framework of Yang--Mills theories of Standard Model. Similarly, the possibility of formulating gravity as the Poincar\'e gauge theory gives the opportunity to produce definite predictions for fermions in the presence of gravitational field. The minimal coupling procedure, however, cannot be applied naively but rather needs to be modified slightly such that it is unambiguous. Application of the corrected coupling method to fermions, together with the inclusion of the Holst term in the gravitational part of the action, leads to the conclusion that the Immirzi parameter is in principle classically measurable, in agreement with the result of Perez and Rovelli., Comment: 5 pages, extended version of proc. of 12 Marcel Grossman meeting

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\'e gauge theory of gravity. In particular, the predictions of the Einstein-Cartan theory with fermionic matter are rendered unique., Comment: 4 pages

The gauge approach to the theory of gravity has been widely discussed as an alternative to standard general relativity. The Poincar{\'e} 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{\'e} 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{\'e} 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., Comment: 15 pages, linguistic corrections

We investigate the consequences of the ambiguity of minimal coupling procedure for Einstein-Cartan gravity with Holst term and fermions. A new insight is provided into the nature and physical relevance of coupling procedures considered hitherto in the context of Ashtekar-Barbero-Immirzi formalism with fermions. The issue of physical effects of the Immirzi parameter in semi--classical theory is reinvestigated. We argue that the conclusive answer to the question of its measurability will not be possible until the more fundamental problem of nonuniqueness of gravity--induced fermion interaction in Einstein-Cartan theory is solved., Comment: 11 pages, typos corrected, final version, to appear in Phys. Rev. D

The problem of nonuniqueness of minimal coupling procedure for Einstein--Cartan (EC) gravity with matter is investigated. It is shown that the predictions of the theory of gravity with fermionic matter can radically change if the freedom of addition of a divergence to the flat space matter Lagrangean density is exploited. The well--known gravity induced four--fermion interaction is shown to reveal unexpected features. The solution to the problem of nonuniqueness of minimal coupling of EC gravity is argued to be necessary in order for the theory to produce definite predictions. In particular, the EC theory with fermions is shown to be indistinguishable from usual General Relativity on the effective level, if the flat space fermionic Lagrangean is appropriately chosen. Hence, the solution to the problem of nonuniqueness of minimal coupling procedure is argued to be necessary if EC theory is to be experimentally verifiable. It could also enable experimental tests of theories based on EC, such as loop approach to quantisation of gravitational field. Some ideas of how the arbitrariness incorporated in EC theory could be restricted or even eliminated are presented., Comment: 13 pages, references added, more exhaustive explanations given, typos corrected

We consider the geometric structures on the moduli space of static finite energy solutions to the 2+1 dimensional unitary chiral model with the Wess-Zummino-Witten (WZW) term. It is shown that the magnetic field induced by the WZW term vanishes when restricted to the moduli spaces constructed from the Grassmanian embeddings, so that the slowly moving solitons can in some cases be approximated by a geodesic motion on a space of rational maps from $\CP^1$ to the Grassmanian., Comment: 19 pages. Final version, to appear in the Journal of Geometry and Physics