A spin network primer
Abstract
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 finite 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 with diagrams. This spin network diagrammatic method offers 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.
 Publication:

American Journal of Physics
 Pub Date:
 November 1999
 DOI:
 10.1119/1.19175
 arXiv:
 arXiv:grqc/9905020
 Bibcode:
 1999AmJPh..67..972M
 Keywords:

 01.50.i;
 03.65.Fd;
 02.40.k;
 02.10.Sp;
 02.20.a;
 Educational aids;
 Algebraic methods;
 Geometry differential geometry and topology;
 Group theory;
 General Relativity and Quantum Cosmology;
 Quantum Physics
 EPrint:
 A review of spin networks suitable for students of advanced quantum mechanics (undergraduate). 16 pages, many eps figures, to be published in Am. J. Phys v2: Updated to include key reference