In the previous chapters we gained some insight into the simple algebraic structure and number-theoretic properties of ladder and rainbow diagrams. Without any further ado, we now want to associate link diagrams to these diagrams. The entanglement of these link diagrams should reflect the topological simplicity of the diagrams.

We ask ourselves how we can encode the topology of a Feynman diagram in a sensible manner. By this we mean the following. We have just learned that the antipodes of PWs corresponding to ladder diagrams have values in ℚ. We suggest that this property reflects the topological simplicity of these words as Feynman diagrams. Let us try to relate these Feynman diagrams to yet another branch of low-dimensional topology, to link diagrams. At this stage, our sole purpose is to play around with such relations and to try out various ways of mapping Feynman diagrams to link diagrams. We will consider two such maps, and will investigate their usefulness in Chapters 7, 8 and 10. The first map is based on the momentum flow in the diagrams. The second relies on the Gauss code of the diagram.

We have not yet defined link diagrams, and postpone a proper definition to Chapter 6. Here we will rely solely on our intuitive understanding of link diagrams.

Link diagrams from ladder diagrams

The iPWs of Chapter 4 were built from one-loop letters.