Volume 99, Number 1, July 2012
|Number of page(s)||6|
|Published online||11 July 2012|
The picture of the Bianchi I model via gauge fixing in Loop Quantum Gravity
1 Institute for Quantum Gravity (IQG), FAU Erlangen-Nürnberg - Staudtstr. 7, 91058 Erlangen, Germany, EU
2 Dipartimento di Fisica, Università di Roma “Sapienza” - Piazzale Aldo Moro 5, 00185 Roma, Italy, EU
3 ENEA, Centro Ricerche Frascati, U.T. Fus. (Fus. Mag. Lab.) - Via Enrico Fermi 45, 00044 Frascati, Roma, Italy, EU
4 INFN, Sezione Roma1 - Piazzale Aldo Moro 5, 00185 Roma, Italy, EU
Received: 12 January 2012
Accepted: 13 June 2012
The implications of the SU(2) gauge fixing associated with the choice of invariant triads in Loop Quantum Cosmology are discussed for a Bianchi I model. In particular, via the analysis of Dirac brackets, it is outlined how the holonomy-flux algebra coincides with the one of Loop Quantum Gravity if paths are parallel to fiducial vectors only. In this way the quantization procedure for the Bianchi I model is performed by applying the techniques developed in Loop Quantum Gravity but restricting the admissible paths. Furthermore, the local character retained by the reduced variables provides a relic diffeomorphisms constraint, whose imposition implies homogeneity on a quantum level. The resulting picture for the fundamental spatial manifold is that of a cubical knot with attached SU(2) irreducible representations. The discretization of geometric operators is outlined and a new perspective for the super-Hamiltonian regularization in Loop Quantum Cosmology is proposed.
PACS: 04.60.Pp – Loop quantum gravity, quantum geometry, spin foams / 98.80.Qc – Quantum cosmology
© EPLA, 2012
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