  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.
