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Journal Article

#### Canonical simplicial gravity

##### Fulltext (public)

1108.1974

(Preprint), 550KB

CQG_29_11_115009.pdf

(Any fulltext), 880KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Dittrich, B., & Hoehn, P. A. (2012). Canonical simplicial gravity.*
Classical and quantum gravity,* *29*(11): 115009. doi:10.1088/0264-9381/29/11/115009.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-14D8-D

##### Abstract

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.