On the possibility of finite quantum Regge calculus

TL;DR

This paper explores finite quantum Regge calculus, showing that the theory's link lengths are dynamically concentrated around the Planck scale, leading to a finite, well-defined quantum gravity model.

Contribution

It demonstrates that quantum Regge calculus can have nonzero, finite link lengths due to the path integral measure, making the theory resemble a lattice field theory with dynamical spacings.

Findings

Vacuum expectation values of link lengths are of Planck scale.

Probability distribution concentrates at finite nonzero link lengths.

The theory behaves like a lattice with fixed spacings, but spacings are dynamical.

Abstract

The arguments were given in a number of our papers that the discrete quantum gravity based on the Regge calculus possesses nonzero vacuum expectation values of the triangulation lengths of the order of Plank scale $10^{-33}cm$. These results are considered paying attention to the form of the path integral measure showing that probability distribution for these linklengths is concentrated at certain nonzero finite values of the order of Plank scale. That is, the theory resembles an ordinary lattice field theory with fixed spacings for which correlators (Green functions) are finite, UV cut off being defined by lattice spacings. The difference with an ordinary lattice theory is that now lattice spacings (linklengths) are themselves dynamical variables, and are concentrated around certain Plank scale values due to {\it dynamical} reasons.