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 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 the Barbero-Immirzi parameter. This provides a topological interpretation for this parameter. Matter coupling can then be introduced in the usual manner, without changing the universal topological Nieh-Yan term.
- Received 6 December 2008
DOI:https://doi.org/10.1103/PhysRevD.79.044008
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