Gauge invariant discretization of Poincare quantum gravity

TL;DR

This paper introduces a gauge-invariant discretization method for Poincare quantum gravity by extending Regge calculus to Riemann-Cartan space, enabling lattice formulations with flat hypercubic pieces.

Contribution

It generalizes Regge calculus to Riemann-Cartan space and constructs a gauge-invariant lattice model for Poincare quantum gravity.

Findings

Derived the lattice action for squared curvature

Constructed a local measure for dynamical variables

Proposed a discretization preserving gauge invariance

Abstract

In this paper we suggest gauge invariant discretization of Poincare quantum gravity. We generalize Regge calculus to the case of Riemann-Cartan space. The basic element of the constructed discretization is piecewize linear Riemann-Cartan space with flat pieces of hypercubic form. We consider the model with squared curvature action and calculate the correspondent lattice action. We construct local measure over the dynamical variables of the lattice model.