A Spin Network Primer

Details A Spin Network Primer A Spin Network Primer

1999-05-06

arxiv.org/abs/gr-qc/9905020v2

Am.J.Phys. 67 (1999) 972-980

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

A review of spin networks suitable for students of advanced quantum mechanics (undergraduate). 16 pages, many eps figures, to

Scientific paper

10.1119/1.19175

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 by 2 matrices to 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.

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