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arXiv · 0907.1530

The Immirzi parameter from an external scalar field

Francesco Cianfrani·Giovanni Montani
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Abstract

We promote the Immirzi parameter to be a minimally coupled scalar field and we analyzed the Hamiltonian constraints in the framework of Loop Quantum Gravity without the time gauge. Proper SU(2) connections can be defined and a term containing derivatives of the field $β$ enters into their definition. Furthermore, boost degrees of freedom are non-dynamical, while the super-momentum constraints coincide with the scalar field case. Hence, the kinematical Hilbert space can be defined as for gravity in presence of a minimally coupled scalar field. Then, we analyzed the dynamical implications of this scenario and we outlined how a the dynamical relaxation to a non-vanishing vacuum expectation value is predicted.

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Francesco Cianfrani, Giovanni Montani. 2009-11-02. The Immirzi parameter from an external scalar field. https://doi.org/10.1103/physrevd.80.084040

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