Effective Theory of Braid Excitations of Quantum Geometry in terms of Feynman Diagrams

TL;DR

This paper develops an effective Feynman diagram-based theory to describe interactions of topologically conserved braid excitations in quantum gravity models, revealing their boson-like behavior and interaction mechanisms.

Contribution

It introduces a novel effective theory using Feynman diagrams to model braid interactions in quantum geometry, connecting topological conservation laws with particle-like behavior.

Findings

Braid excitations propagate and interact in spin foam models.

Active braids behave like bosons, being created and destroyed singly.

Interactions involve charge exchanges under topological conservation.

Abstract

We study interactions amongst topologically conserved excitations of quantum theories of gravity, in particular the braid excitations of four-valent spin networks. These have been shown previously to propagate and interact under evolution rules of spin foam models. We show that the dynamics of these braid excitations can be described by an effective theory based on Feynman diagrams. In this language, braids which are actively interacting are analogous to bosons, in that the topological conservation laws permit them to be singly created and destroyed. Exchanges of these excitations give rise to interactions between braids which are charged under the topological conservation rules.