There's an interesting series of papers by Bahr and Dittrich, and a related video talk by Dittrich at the Planck Scale site. The papers bear on issues discussed in the Lewandowski thread. The first in the series is a good introduction to the rest. Here are some links and abstracts to show what is talked about: http://arxiv.org/abs/0810.3594 Diffeomorphism symmetry in quantum gravity models Bianca Dittrich Invited constribution to a special issue of Advanced Science Letters, 16 pages (Submitted on 20 Oct 2008) "We review and discuss the role of diffeomorphism symmetry in quantum gravity models. Such models often involve a discretization of the space-time manifold as a regularization method. Generically this leads to a breaking of the symmetries to approximate ones, however there are incidences in which the symmetries are exactly preserved. Both kind of symmetries have to be taken into account in covariant and canonical theories in order to ensure the correct continuum limit. We will sketch how to identify exact and approximate symmetries in the action and how to define a corresponding canonical theory in which such symmetries are reflected as exact and approximate constraints." http://arxiv.org/abs/0905.1670 (Broken) Gauge Symmetries and Constraints in Regge Calculus Benjamin Bahr, Bianca Dittrich 32 pages, 15 figures (Submitted on 11 May 2009) "We will examine the issue of diffeomorphism symmetry in simplicial models of (quantum) gravity, in particular for Regge calculus. We find that for a solution with curvature there do not exist exact gauge symmetries on the discrete level. Furthermore we derive a canonical formulation that exactly matches the dynamics and hence symmetries of the covariant picture. In this canonical formulation broken symmetries lead to the replacements of constraints by so--called pseudo constraints. These considerations should be taken into account in attempts to connect spin foam models, based on the Regge action, with canonical loop quantum gravity, which aims at implementing proper constraints. We will argue that the long standing problem of finding a consistent constraint algebra for discretized gravity theories is equivalent to the problem of finding an action with exact diffeomorphism symmetries. Finally we will analyze different limits in which the pseudo constraints might turn into proper constraints. This could be helpful to infer alternative discretization schemes in which the symmetries are not broken." http://arxiv.org/abs/0907.4323 Improved and Perfect Actions in Discrete Gravity Benjamin Bahr, Bianca Dittrich 28 pages, 2 figures (Submitted on 24 Jul 2009) "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." http://arxiv.org/abs/0907.4325 Regge calculus from a new angle Benjamin Bahr, Bianca Dittrich 8 pages (Submitted on 24 Jul 2009) "In Regge calculus space time is usually approximated by a triangulation with flat simplices. We present a formulation using simplices with constant sectional curvature adjusted to the presence of a cosmological constant. As we will show such a formulation allows to replace the length variables by 3d or 4d dihedral angles as basic variables. Moreover we will introduce a first order formulation, which in contrast to using flat simplices, does not require any constraints. These considerations could be useful for the construction of quantum gravity models with a cosmological constant."