Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-08-09
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
52 pages, 14 figures, 3 tables
Scientific paper
A general canonical formalism for discrete systems is developed which can handle varying phase space dimensions and constraints. The central ingredient is Hamilton's principle function which generates canonical time evolution and ensures that the canonical formalism reproduces the dynamics of the covariant formulation following directly from the action. We apply this formalism to simplicial gravity and (Euclidean) Regge calculus, in particular. A discrete forward/backward evolution is realized by gluing/removing single simplices step by step to/from a bulk triangulation and amounts to Pachner moves in the triangulated hypersurfaces. As a result, the hypersurfaces evolve in a discrete `multi-fingered' time through the full Regge solution. Pachner moves are an elementary and ergodic class of homeomorphisms and generically change the number of variables, but can be implemented as canonical transformations on naturally extended phase spaces. Some moves introduce a priori free data which, however, may become fixed a posteriori by constraints arising in subsequent moves. The end result is a general and fully consistent formulation of canonical Regge calculus, thereby removing a longstanding obstacle in connecting covariant simplicial gravity models to canonical frameworks. The present scheme is, therefore, interesting in view of many approaches to quantum gravity, but may also prove useful for numerical implementations.
Dittrich Bianca
Hoehn Philipp A.
No associations
LandOfFree
Canonical simplicial gravity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Canonical simplicial gravity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Canonical simplicial gravity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-70520