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The Classical and Quantum 6"J"-symbols
Author: J. Scott Carter

ISBN: 9780691027302
Format: Paperback
Number Of Pages: 176
Published: 16 November 1995
Country of Publication: US
Dimensions (cm): 22.9 x 15.2 x 1.0
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 6"j"-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 paramet...

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