The Classical and Quantum 6j-symbols

J. Scott Carter, Daniel E. Flath, Masahico Saito

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English

Princeton University Press
12 March 1996

Applied mathematics; Quantum physics (quantum mechanics & quantum field theory)

Series: Mathematical Notes

Addressing physicists and mathematicians alike, this book discusses the finite dimensional representation theory of sl(2), both classical and quantum. Covering representations of U(sl(2)), quantum sl(2), the quantum trace and color representations, and the Turaev-Viro invariant, this work is useful to graduate students and professionals. The classic subject of representations of U(sl(2)) is equivalent to the physicists' theory of quantum angular momentum. This material is developed in an elementary way using spin-networks and the Temperley-Lieb algebra to organize computations that have posed difficulties in earlier treatments of the subject. The emphasis is on the 6j-symbols and the identities among them, especially the Biedenharn-Elliott and orthogonality identities. The chapter on the quantum group Uq(sl(2)) develops the representation theory in strict analogy with the classical case, wherein the authors interpret the Kauffman bracket and the associated quantum spin-networks algebraically. The authors then explore instances where the quantum parameter q is a root of unity, which calls for a representation theory of a decidedly different flavor.

The theory in this case is developed, modulo the trace zero representations, in order to arrive at a finite theory suitable for topological applications.

The Turaev-Viro invariant for 3-manifolds is defined combinatorially using the theory developed in the preceding chapters. Since the background from the classical, quantum, and quantum root of unity cases has been explained thoroughly, the definition of this invariant is completely contained and justified within the text.

By: J. Scott Carter, Daniel E. Flath, Masahico Saito
Imprint: Princeton University Press
Country of Publication: United States
Volume: 43
Dimensions: Height: 235mm, Width: 152mm, Spine: 11mm
Weight: 255g
ISBN: 9780691027302
ISBN 10: 0691027307
Series: Mathematical Notes
Pages: 176
Publication Date: 12 March 1996
Audience: Professional and scholarly , College/higher education , Undergraduate , Primary
Format: Paperback
Publisher's Status: Active

J. Scott Carter is Associate Professor and Daniel E. Flath is Associate Professor, both in the Department of Mathematics at the University of South Alabama. Masahico Saito is Assistant Professor of Mathematics at the University of South Florida.

Reviews for The Classical and Quantum 6j-symbols

Overall this book would serve as an excellent introduction for students or mathematicians to any of the subjects included (representation theory of U(sl2) and Uq(sl2), Penrose/Kauffman style diagrammatics, Turaev-Viro theory). . . --Mathematical Reviews