Phase space descriptions for simplicial 4D geometries

By B. Dittrich, J. Patrick Ryan. 2008

147 citations recorded by the source corpus.

Starting from the canonical phase space for discretized (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 with 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 in [1] (prior to the imposition of gluing constraints, which ensure the metricity of the triangulation). Finally, we show that for a subclass of triangulations one can construct first-class Hamiltonian and diffeomorphism constraints leading to flat 4D spacetimes.

Subfields: Neurology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f640e046d74c6485410edd169006ab9a62194c94

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Citations in the corpus

Polyhedra in loop quantum gravity (2010, background): “For the special case in which all the polyhedra are tetrahedra, this is the set-up (13)Aspects of this discontinuity have been discussed also in [39, 40]”
Twistors to twisted geometries (2010, background): “The description provides a natural extension of Regge geometries allowing for discontinuous metrics [1] (See also [2, 3]).”
Improved and Perfect Actions in Discrete Gravity (2009, background): “We do this by considering the ODE’s that the two improved actions (5.7) and (5.14) satisfy, and show that in the continuum limit they converge to each other.”
The Spin-Foam Approach to Quantum Gravity (2012, background): “This question is quite an important one and has been one of the central concerns of the work led by Dittrich and collaborators for the last few years [151, 147, 150, 144, 43].”
Twisted geometries: A geometric parametrisation of SU(2) phase space (2010, methodology): “Furthermore, the construction of a phase space for Regge calculus has been investigated by Bahr, Dittrich and Ryan [20, 35] (see also [36]).”