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The Classical and Quantum 6j-symbols. (MN-43), Volume 43

Paperback / softback

Main Details

Title The Classical and Quantum 6j-symbols. (MN-43), Volume 43
Authors and Contributors      By (author) J. Scott Carter
By (author) Daniel E. Flath
By (author) Masahico Saito
SeriesMathematical Notes
Physical Properties
Format:Paperback / softback
Pages:176
Dimensions(mm): Height 235,Width 152
Category/GenreApplied mathematics
Quantum physics
ISBN/Barcode 9780691027302
ClassificationsDewey:510
Audience
Professional & Vocational
Tertiary Education (US: College)

Publishing Details

Publisher Princeton University Press
Imprint Princeton University Press
Publication Date 31 December 1995
Publication Country United States

Description

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.

Author Biography

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

"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