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

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