Topological Interpretation of Barbero-Immirzi Parameter
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.
Cite
@article{arxiv.0811.4496,
title = {Topological Interpretation of Barbero-Immirzi Parameter},
author = {Ghanashyam Date and Romesh K. Kaul and Sandipan Sengupta},
journal= {arXiv preprint arXiv:0811.4496},
year = {2009}
}
Comments
14 pages, revtex4, no figures. Minor modifications with additional remarks. References rearranged