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.

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

References in corpus (3)

• Canonical Gravity with Fermions
• From the Einstein-Cartan to the Ashtekar-Barbero canonical constraints, passing through the Nieh-Yan functional
• Holst Actions for Supergravity Theories

Cited by in corpus (2)

• Barbero-Immirzi field in canonical formalism of pure gravity
• Peccei--Quinn mechanism in gravity and the nature of the Barbero--Immirzi parameter