Topological Interpretation of Barbero-Immirzi Parameter

Details Topological Interpretation of Barbero-Immirzi Parameter Topological Interpretation of Barbero-Immirzi Parameter

2008-11-27

arxiv.org/abs/0811.4496v2

Phys.Rev.D79:044008,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, revtex4, no figures. Minor modifications with additional remarks. References rearranged

Scientific paper

10.1103/PhysRevD.79.044008

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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