Two-Dimensional Lattice Gravity as a Spin System
W. Beirl, H. Markum, J. Riedler
TL;DR
This paper explores a novel approach to quantum gravity by transforming the path integral in Regge calculus into a spin system on a Kagome lattice, considering various measures and extensions.
Contribution
It introduces a new formulation of quantum gravity as a spin system derived from lattice gravity, with analysis of measures and potential extensions.
Findings
Path integral mapped to Kagome lattice spin system
Different measures act as external fields in the model
Extensions to matter fields and higher dimensions discussed
Abstract
Quantum gravity is studied in the path integral formulation applying the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin system with higher couplings on a Kagome lattice. Various measures acting as external field are considered. Extensions to matter fields and higher dimensions are discussed.
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