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 (13)

• Real Ashtekar Variables for Lorentzian Signature Space-times
• Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
• Real and complex connections for canonical gravity
• Quantum Gravity, Torsion, Parity Violation and all that
• Physical effects of the Immirzi parameter
• Topological Invariants, Instantons and Chiral Anomaly on Spaces with Torsion
• Fermions in Ashtekar-Barbero Connections Formalism for Arbitrary Values of the Immirzi Parameter
• SO(4,C)-covariant Ashtekar-Barbero gravity and the Immirzi parameter
• Hamiltonian analysis of General relativity with the Immirzi parameter
• Canonical Gravity with Fermions
• From the Einstein-Cartan to the Ashtekar-Barbero canonical constraints, passing through the Nieh-Yan functional
• Yang-Mills analogues of the Immirzi ambiguity
• Holst Actions for Supergravity Theories

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