Canonical simplicial gravity

Understand

A general canonical formalism for discrete systems is developed which can handle varying phase space dimensions and constraints.

• The central ingredient is Hamilton's principal 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.