A complete canonical formulation is given for Pontryagin and Euler classes with the Barbero-Immirzi parameter, recovering the self-dual case at imaginary values and coupling the invariants to the Holst action.
Montesinos, Class.Quant.Grav
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Canonical description of Pontryagin and Euler classes with a Barbero-Immirzi parameter
A complete canonical formulation is given for Pontryagin and Euler classes with the Barbero-Immirzi parameter, recovering the self-dual case at imaginary values and coupling the invariants to the Holst action.