2008/07/31 by Bianca Dittrich, James P. Ryan · 1 citation
Physics and Astronomy · #gr-qc
paper · pdf · doi:10.1088/0264-9381/28/6/065006
published as Class.Quant.Grav.28:065006,2011 · corrected structure constants, several references add
arxiv created 2010/06/17 · arxiv updated 2011/03/03
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.