Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-12-09
Class.Quant.Grav.27:155001,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
37 pages, 5 figures (minor modifications, matches published version + updated references)
Scientific paper
10.1088/0264-9381/27/15/155001
Starting from an action for discretized gravity we derive a canonical formalism that exactly reproduces the dynamics and (broken) symmetries of the covariant formalism. For linearized Regge calculus on a flat background -- which exhibits exact gauge symmetries -- we derive local and first class constraints for arbitrary triangulated Cauchy surfaces. These constraints have a clear geometric interpretation and are a first step towards obtaining anomaly--free constraint algebras for canonical lattice gravity. Taking higher order dynamics into account the symmetries of the action are broken. This results in consistency conditions on the background gauge parameters arising from the lowest non--linear equations of motion. In the canonical framework the constraints to quadratic order turn out to depend on the background gauge parameters and are therefore pseudo constraints. These considerations are important for connecting path integral and canonical quantizations of gravity, in particular if one attempts a perturbative expansion.
Dittrich Bianca
Hoehn Philipp A.
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