Reflection positivity in simplicial gravity

Abstract

Within the context of piecewise linear manifolds we establish reflection positivity with a Hilbert action given in terms of the Regge curvature and a cosmological term. Using this positivity a Hilbert space for a quantum theory is constructed and some field operators and observables are given. The set-up allows to introduce time reversal though no time exists. All constructions are non-perturbative.