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 nondynamical, while the supermomentum 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 outline how a dynamical relaxation to a nonvanishing vacuum expectation value is predicted, so recovering the standard loop quantum gravity formulation. © 2009 The American Physical Society.
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|Publication status||Published - 28 Oct 2009|
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
Cianfrani, F., & Montani, G. (2009). Immirzi parameter from an external scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology, 80(8), -. . https://doi.org/10.1103/PhysRevD.80.084040