Ricci curvature and quantum geometry

Abstract

We describe a few elementary aspects of the circle of ideas associated with a quantum field theory (QFT) approach to Riemannian Geometry, a theme related to how Riemannian structures are generated out of the spectrum of (random or quantum) fluctuations around a background fiducial geometry. In such a scenario, Ricci curvature with its subtle connections to diffusion, optimal transport, Wasserestein geometry, and renormalization group, features prominently.

11 pages

References in corpus (2)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds