Unitarity of 4D Lattice Theory of Gravity

TL;DR

This paper proves the unitarity of a 4D lattice gravity theory with Minkowski signature, establishing it as a valid discrete regularization of Einstein-Cartan-Palatini gravity.

Contribution

It provides a direct lattice proof of unitarity for 4D lattice gravity in Minkowski space, connecting Euclidean and Minkowski signatures via contour deformation.

Findings

Unitarity is proven for the lattice theory in Minkowski signature.

The lattice theory reduces to Einstein-Cartan-Palatini in the long-wave limit.

The result supports the lattice theory as a valid regularization of continuous gravity.

Abstract

The unitarity of the 4D lattice theory of gravity in the case of the Minkowski signature is proved. The proof is valid only for lattices that conserve the number of degrees of freedom during time evolution. The Euclidean signature and the Minkowski signature are related by the deformation of the integration contours of dynamic variables in a discrete lattice functional integral. It is important that the result is obtained directly on the lattice. Since the studied lattice theory of gravity in the long-wave limit transforms into the well-known Einstein-Cartan-Palatini theory, the obtained result means that this lattice theory of gravity has the right to be considered as a discrete regularization of the generally accepted continuous physical theory of gravity.