Consistent discretization and canonical classical and quantum Regge calculus

TL;DR

This paper introduces a consistent discretization approach to Regge calculus for general relativity, resulting in a constraint-free canonical theory suitable for quantum gravity and topology change analysis.

Contribution

It develops a well-defined canonical formulation of Regge calculus that is constraint-free and applicable to both Euclidean and Lorentzian cases, advancing quantum gravity research.

Findings

Constraint-free canonical theory for Regge calculus.

Framework for topology change in quantum gravity.

Natural avoidance of spikes in Lorentzian case.

Abstract

We apply the ``consistent discretization'' technique to the Regge action for (Euclidean and Lorentzian) general relativity in arbitrary number of dimensions. The result is a well defined canonical theory that is free of constraints and where the dynamics is implemented as a canonical transformation. This provides a framework for the discussion of topology change in canonical quantum gravity. In the Lorentzian case, the framework appears to be naturally free of the ``spikes'' that plague traditional formulations. It also provides a well defined recipe for determining the measure of the path integral.