1998/07/30 by E. Bittner, A. Hauke, C. Holm +3
Physics and Astronomy · #hep-lat
published as Frontiers in Quantum Physics (Springer 1998) pp. 303 · 4 pages, 1 figures
arxiv created 1998/07/30 · arxiv updated 2009/12/01
Standard Regge Calculus provides an interesting method to explore quantum gravity in a non-perturbative fashion but turns out to be a CPU-time demanding enterprise. One therefore seeks for suitable approximations which retain most of its universal features. The Z2-Regge model could be such a desired simplification. Here the quadratic edge lengths q of the simplicial complexes are restricted to only two possible values q=1+εσ, with σ=± 1, in close analogy to the ancestor of all lattice theories, the Ising model. To test whether this simpler model still contains the essential qualities of the standard Regge Calculus, we study both models in two dimensions and determine several observables on the same lattice size. In order to compare expectation values, e.g. of the average curvature or the Liouville field susceptibility, we employ in both models the same functional integration measure. The phase structure is under current investigation using mean field theory and numerical simulation.