In [1] and [2] models of elementary particles are proposed based on combinatorial substructures for quarks.
These papers succeed in given combinatorial models for many particle interactions. In [3] a vector version of the Harari, Shupe models is 
given, in which each particle is a four-vector and particle interactions correspond to vector identities. The Lambek model can be matched directly with the Shupe model, but contains 
extra information that allows the vectorial work. In [4] a so-called Helon model is given by Bilson-Thompson that uses framed three braids and can be seen as a generalization of the Rishon models of Harari and Schupe. In fact, we find (joint work with David Chester and Xerxes Arsiwalla) that the Lambek model is a nearly perfect intermediary between the Helon model and the Rishon model. There is a direct correspondence between Lambek's four-vectors and the braids in the Helon model, up to a slight readjustment. This means that we are in possession of a dictionary that lets us discuss and compare the structures in these models and to examine possible generalizations of them. We also can use this point of view to see some of the limitations of the Helon model that arise from the non-commutativity of the Artin Braid Group. The talk will present these structures, and our speculations about generalizations and relationships with other topological work such as found in the papers of the author [5], the work of Witten [6] and alternate topological intepretations such as [7], [8], [9] and [10].

This paper examines the structure of the Dirac equation and gives a new treatment of the Dirac equation in 1+1 spacetime.

We reformulate the Dirac operator (using the method of Peter Rowlands) so that there is a nilpotent element in the Clifford algebra such that for a plane wave, the Dirac operator applied to the plane wave returns the wave multiplied by the nilpotent element.

This means that the product of the nilpotent element and the plane wave is a solution to the Dirac equation. We use this formulation to produce solutions of the Dirac equation for (1+1) spacetime in light cone coordinates. We compare and raise questions about this solution in relation to the solutions already understood via the Feynman checkerboard model. We show that the transition to light cone coordinates corresponds to a rewriting of the Clifford algebra for the Dirac equation to a Fermionic algebra linked with a Clifford algebra.