Statistical mechanical space-time decomposition as a key to a (non-perturbative) quantization prescription for gravity

Abstract

By assuming gravity and matter to be subject to a joint statistical mechanical concept (JSMC) and interpreting Rindler horizon sections as open thermodynamic systems, one arrives at a specific new form of non-perturbative Lorentzian path integral quantisation in a compact space-time region, with well-determined gravitational measure, adequate fixing of boundary conditions and causal geometries. JSMC implies a space-time decomposition, leading to a sum over configurations in line with path integral methods. In these developments, we carefully distinguish the concepts of Boltzmann's statistical mechanics and the path integral.