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2008

Topological Interpretation of Barbero-Immirzi Parameter

Date, Ghanashyam, Kaul, Romesh K., Sengupta, Sandipan

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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.

Topological Interpretation of Barbero-Immirzi Parameter · Around

Built on

A. Ashtekar, New Variables For Classical And Quantum Gravity, Phys. Rev. Lett. 57
1987
Earlier work this paper cites.
J. Fernando G. Barbero, Real Ashtekar Variables for Lorentzian Signature Space-times, Phys. Rev. D51
1995
Earlier work this paper cites.
S. Holst, Barbero’s Hamiltonian Derived from a Generalized Hilbert-Palatini Action, Phys. Rev. D53
1996
Earlier work this paper cites.
Giorgio Immirzi, Real and Complex Connections for Canonical Gravity, Class. Quant. Grav. 14
1997
Earlier work this paper cites.

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Then

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Romesh K. Kaul, Holst Actions for Supergravity Theories, Phys. Rev. D77
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