Unitarity of 4D Lattice Theory of 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.

arXiv comment11 pages, 1 figure

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