The Immirzi parameter from an external scalar field

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 $\beta$ 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.

5 pages

References in corpus (5)

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• Barbero-Immirzi field in canonical formalism of pure gravity
• Peccei--Quinn mechanism in gravity and the nature of the Barbero--Immirzi parameter
• Towards Loop Quantum Gravity without the time gauge
• Background independent quantizations: the scalar field II