Spikes in Quantum Regge Calculus

TL;DR

This paper shows that in two-dimensional quantum Regge calculus, the measure is highly non-local, leading to degenerate spikes and the failure to recover continuum quantum gravity results, raising concerns for higher-dimensional applications.

Contribution

It explicitly calculates the DeWitt-like measure in 2D quantum Regge gravity, revealing fundamental issues with length definitions and measure behavior.

Findings

The measure is highly non-local in 2D quantum Regge gravity.

Average link lengths do not exist for high powers, indicating degeneracy.

The formalism fails to reproduce continuum results, suggesting problems in higher dimensions.

Abstract

We demonstrate by explicit calculation of the DeWitt-like measure in two-dimensional quantum Regge gravity that it is highly non-local and that the average values of link lengths $l, <l^n>$, do not exist for sufficient high powers of $n$. Thus the concept of length has no natural definition in this formalism and a generic manifold degenerates into spikes. This might explain the failure of quantum Regge calculus to reproduce the continuum results of two-dimensional quantum gravity. It points to severe problems for the Regge approach in higher dimensions.