A spin network primer

Spin networks, essentially labeled graphs, are "good quantum numbers" for t he quantum theory of geometry. These structures encompass a diverse range o f techniques which may be used in the quantum mechanics of finite dimension al systems, gauge theory, and knot theory. Though accessible to undergradua tes, spin network techniques are buried in more complicated formulations. I n this paper a diagrammatic method, simple but rich, is introduced through an association of 2 X 2 matrices with diagrams. This spin network diagramma tic method offers new perspectives on the quantum mechanics of angular mome ntum, group theory, knot theory, and even quantum geometry. Examples in eac h of these areas are discussed. (C) 1999 American Association of Physics Te achers.