arXiv subjects

A. Hauke

Publications and source records attributed to A. Hauke.

4 recordsLinked to original sources

arXiv1999

Z_2-Regge versus Standard Regge Calculus in two dimensions

We consider two versions of quantum Regge calculus. The Standard Regge Calculus where the quadratic link lengths of the simplicial manifold vary continuously and the Z_2-Regge Model where they are restricted to two possible values. The goal is to determine whether the computationally more easily accessible Z_2 model still retains the universal characteristics of standard Regge theory in two dimensions. In order to compare observables such as average curvature or Liouville field susceptibility, we use in both models the same functional integration measure, which is chosen to render the Z_2-Regge Model particularly simple. Expectation values are computed numerically and agree qualitatively for positive bare couplings. The phase transition within the Z_2-Regge Model is analyzed by mean-field theory.

hep-lat↗

arXiv1998

Lattice Models of Quantum Gravity

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 $Z_2$-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 $σ=\pm 1$, 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.

hep-lat↗

arXiv1996

Correlation functions in lattice formulations of quantum gravity

We compare different models of a quantum theory of four-dimensional lattice gravity based on Regge's original proposal. From Monte Carlo simulations we calculate two-point functions between geometrical quantities and estimate the masses of the corresponding interaction particles.

hep-lat↗

arXiv1995

The phase structure of pure Regge gravity

We examine the phase structure of pure Regge gravity in four dimensions and compare our Monte Carlo results with $Z_2$-link Regge-theory as well as with another formulation of lattice gravity derived from group theoretical considerations. Within all three models we find an extension of the well-defined phase to negative gravitational coupling and a new phase transition. In contrast to the well-known transition at positive coupling there is evidence for a continuous phase transition which might be essential for a possible continuum limit.

hep-lat↗