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arXiv · 0811.4496

Topological Interpretation of Barbero-Immirzi Parameter

Ghanashyam Date·Romesh K. Kaul·Sandipan Sengupta
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Abstract

We set up a canonical Hamiltonian formulation for a theory of gravity based on a Lagrangian density made up of the Hilbert-Palatini term and, instead of the Holst term, the Nieh-Yan topological density. The resulting set of constraints in the time gauge are shown to lead to a theory in terms of a real SU(2) connection which is exactly the same as that of Barbero and Immirzi with the coefficient of the Nieh-Yan term identified as the inverse of Barbero-Immirzi parameter. This provides a topological interpretation for this parameter. Matter coupling can then be introduced in the usual manner, {\em without} changing the universal topological Nieh-Yan term.

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Ghanashyam Date, Romesh K. Kaul, Sandipan Sengupta. 2008-12-04. Topological Interpretation of Barbero-Immirzi Parameter. https://doi.org/10.1103/physrevd.79.044008

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