Quantum wormhole as a Ricci flow

TL;DR

This paper proposes that quantum wormholes in spacetime foam can be modeled using Ricci flow, interpreting the flow as a statistical system where each metric represents a microscopic state linked to Perelman's functional.

Contribution

It introduces a novel interpretation of quantum wormholes as Ricci flows, connecting geometric evolution with statistical and quantum properties.

Findings

Ricci flow models quantum wormholes in spacetime foam.

Microscopic states correspond to metrics in the Ricci flow.

Perelman's functional relates to the probability density of states.

Abstract

The idea is considered that a quantum wormhole in a spacetime foam can be described as a Ricci flow. In this interpretation the Ricci flow is a statistical system and every metric in the Ricci flow is a microscopical state. The probability density of the microscopical state is connected with a Perelman's functional of a rescaled Ricci flow.