Fractal structure in two-dimensional quantum Regge calculus

Fractal Structure in Two-Dimensional Quantum Regge Calculus

We study the fractal structure of the surface in two-dimensional quantum Regge calculus by performing Monte Carlo simulation with up to 200,000 triangles. The result E-mail address : [email protected], JSPS Research Fellow. E-mail address : [email protected] can be compared with the universal scaling function obtained analytically in the continuum limit of dynamical triangulatio...

Z2-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 Z2 Regge model where they are restricted to two possible values. The goal is to determine whether the computationally more easily accessible Z2 model still retains the universal characteristics of standard Regge theory in two dimen...

Failure of the Regge approach in two dimensional quantum gravity

Regge’s method for regularizing euclidean quantum gravity is applied to two dimensional gravity. We use two different strategies to simulate the Regge path integral at a fixed value of the total area: A standard Metropolis simulation combined with a histogramming method and a direct simulation using a Hybrid Monte Carlo algorithm. Using topologies with genus zero and two and a scale invariant i...

Dynamical Regge Calculus as Lattice Quantum Gravity

We propose a hybrid model of simplicial quantum gravity by performing at once dynamical triangulations and Regge calculus. A motive for the hybridization is to give a dynamical description of topology-changing processes of Euclidean spacetime. In addition, lattice diffeomorphisms as invariance of the simplicial geometry are generated by certain elementary moves in the model. We attempt also a l...

Lens spaces in the Regge calculus approach to quantum cosmology.