Euclidean Quantum Gravity from Variational Dynamics

TL;DR

This paper develops a variational phase space framework for Euclidean quantum gravity on piecewise flat manifolds, enabling numerical sampling of the Euclidean path integral through symplectic flow integration.

Contribution

It introduces a novel variational phase space and action functional that generate a symplectic flow for Euclidean quantum gravity, facilitating numerical sampling.

Findings

Constructed a variational phase space for piecewise flat manifolds

Defined an extended action functional producing symplectic flow

Demonstrated numerical integration of the flow to sample the path integral

Abstract

A variational phase space is constructed for a compact and piecewise flat Riemannian manifold. An extended action functional is provided such that the variational dynamics generate a symplectic flow on the phase space. This symplectic flow is numerically integrated as it evolves with respect to the variational parameter. Assuming ergodicity, the resulting flow samples the Euclidean path integral.