Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-07-17
Class.Quant.Grav.28:065006,2011
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
corrected structure constants, several references add
Scientific paper
10.1088/0264-9381/28/6/065006
Starting from the canonical phase space for discretised (4d) BF-theory, we implement a canonical version of the simplicity constraints and construct phase spaces for simplicial geometries. Our construction allows us to study the connection between different versions of Regge calculus and approaches using connection variables, such as loop quantum gravity. We find that on a fixed triangulation the (gauge invariant) phase space associated to loop quantum gravity is genuinely larger than the one for length and even area Regge calculus. Rather, it corresponds to the phase space of area-angle Regge calculus, as defined by Dittrich and Speziale in [arXiv:0802.0864] (prior to the imposition of gluing constraints, that ensure the metricity of the triangulation). We argue that this is due to the fact that the simplicity constraints are not fully implemented in canonical loop quantum gravity. Finally, we show that for a subclass of triangulations one can construct first class Hamiltonian and Diffeomorphism constraints leading to flat 4d space-times.
Dittrich Bianca
Ryan James P.
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