Improved and Perfect Actions in Discrete Gravity

By Benjamin Bahr, B. Dittrich. 2009

145 citations recorded by the source corpus.

We consider the notion of improved and perfect actions within Regge calculus. These actions are constructed in such a way that they - although being defined on a triangulation - reproduce the continuum dynamics exactly, and therefore capture the gauge symmetries of General Relativity. We construct the perfect action in three dimensions with cosmological constant, and in four dimensions for one simplex. We conclude with a discussion about Regge Calculus with curved simplices, which arises naturally in this context.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0157c64dc92bbbfb1ee8a1133ce9864810f66d54

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Citations in the corpus

The Spin-Foam Approach to Quantum Gravity (2012, background): “In the simple case of 3D gravity with cosmological constant, this can be shown explicitly at the classical level [45] as well as at the quantum level [304].”
Zakopane lectures on loop gravity (2011, background): “23 22This is because the discretization is in the “perfect action" form, in the language of [94].”
Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions (2012, methodology): “Related work on the continuum limit of spin foammodels and discrete gravity path integrals, from a lattice gauge theory perspective, is being carried out by Dittrich and collaborators [54,55].”
Phase space descriptions for simplicial 4D geometries (2008, background): “Although there is a considerable amount of work addressing these questions in different frameworks [11, 14, 15, 16, 17, 18, 19, 20], in our view the issue is not yet settled, even at the classical level.”
The continuum limit of loop quantum gravity - a framework for solving the theory (2014, methodology): “Several examples [21, 20] and arguments (see section 6) show that in particular diffeomorphism symmetry is likely to be restored, which addresses problem (a).”