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 ...
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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 Ub-3.0 qb0(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.
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Add this copy of The Classical and Quantum 6j-Symbols to cart. $71.81, new condition, Sold by Paperbackshop rated 4.0 out of 5 stars, ships from Bensenville, IL, UNITED STATES, published 1996 by Princeton University Press.
Add this copy of The Classical and Quantum 6j-Symbols. (Mn-43), Volume to cart. $70.71, new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 1995 by Princeton University Press.
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New. 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, it is useful to graduate students and professionals. Series: Mathematical Notes. Num Pages: 176 pages, Illustrations. BIC Classification: PBW; PHQ. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 229 x 152 x 11. Weight in Grams: 257. 1995. First Edition. Paperback.....We ship daily from our Bookshop.
Add this copy of The Classical and Quantum 6j-Symbols to cart. $89.24, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 1995 by Princeton University Press.
