Quantum kinematics of the Chern-Simons field with matter in the loop representation

This paper reports on the scalar field coupled to the Abelian Chern-Simons gauge field that is quantized in the loop representation. The physical space of states is found to be labeled by equivalence classes of sets of open paths. The relations among them are studied, showing that the long range interaction provided by the gauge field gives rise to a topological interaction among the paths which is explicitly computed