SU(2) Loop Quantum Gravity seen from Covariant Theory - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Physical Review D Année : 2003

SU(2) Loop Quantum Gravity seen from Covariant Theory

Résumé

Covariant loop gravity comes out of the canonical analysis of the Palatini action and the use of the Dirac brackets arising from dealing with the second class constraints (``simplicity\'\' constraints). Within this framework, we underline a quantization ambiguity due to the existence of a family of possible Lorentz connections. We show the existence of a Lorentz connection generalizing the Ashtekar-Barbero connection and we loop-quantize the theory showing that it leads to the usual SU(2) Loop Quantum Gravity and to the area spectrum given by the SU(2) Casimir. This covariant point of view allows to analyze closely the drawbacks of the SU(2) formalism: the quantization based on the (generalized) Ashtekar-Barbero connection breaks time diffeomorphisms and physical outputs depend non-trivially on the embedding of the canonical hypersurface into the space-time manifold. On the other hand, there exists a true space-time connection, transforming properly under all diffeomorphisms. We argue that it is this connection that should be used in the definition of loop variables. However, we are still not able to complete the quantization program for this connection giving a full solution of the second class constraints at the Hilbert space level. Nevertheless, we show how a canonical quantization of the Dirac brackets at a finite number of points leads to the kinematical setting of the Barrett-Crane model, with simple spin networks and an area spectrum given by the SL(2,C) Casimir.

Dates et versions

hal-00008367 , version 1 (02-09-2005)

Identifiants

Citer

Sergei Alexandrov, Etera R. Livine. SU(2) Loop Quantum Gravity seen from Covariant Theory. Physical Review D, 2003, 67, pp.044009. ⟨10.1103/PhysRevD.67.044009⟩. ⟨hal-00008367⟩
390 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More