Spin Network Primer

Major S.A.

Spin networks, essentially labeled graphs, are good quantum numbers” for the quantum theory of geometry. These structures encompass a diverse range of techniques which may be used in the quantum mechanics of ♀nite dimensional systems, gauge theory, and knot theory. Though accessible to undergraduates, spin network techniques are buried in more complicated formulations. In this paper a diagrammatic method, simple but rich, is introduced through an association of 2☻2 matrices to diagrams. This spin network diagrammatic method o♂ers new perspectives on the quantum mechanics of angular momentum, group theory, knot theory, and even quantum geometry. Examples in each of these areas are discussed.