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

Customer Reviews:

Great book, great service

By S. L. Starr - July 12, 2010

This book arrived from the book seller extremely fast. I ordered it at the end of a trip to visit a colleague, and it was in my mailbox by the time I got home. The trip took a few days. I'm a fan of Amazon's used book service. The book is very nice. It is a nice supplement to Kaufman and Lins's book about Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds. It is also nice to read in conjunction with Frenkel and Khovanov's Duke paper on the graphical representation of the dual canonical basis. I particularly like this book's pictures, such as the movie/cartoon type picture of moving 2-complexes to explain the 6j symbols as relating to the skeleton of the tetrahedron. I also like the graphical proof of the Elliott-Biedenharn identity. I have a few questions about all these things that do not appear in the books. For example, in Theorem 3.12(1) they state an identity for a sum with an alternating sign. Is this also related to Rota's q-analogue of the principal of inclusion,... read more

Good introduction to topological quantum field theory

By Dr. Lee D. Carlson - June 3, 2001

This book is an excellent introduction to the concepts and techniques used to define invariants of closed 3-dimensional manifolds using the representation theory of U(sl(2)). Starting with the well-known results in the finite-dimensional irreducible representations of SL(2) via the Clebsch-Gordan theory, one can decompose the tensor product of these representations in two ways. The two decompositions can be compared using recoupling theory, with the coefficients being the ubiquitous 6j-symbols, so familiar to physicists in the theory of angular momentum. The orthogonality and Elliott-Biedenharn identities of the 6j-symbols have a geometric interpretation as the union of two tetrahedra. The quantum analog of these results for sl(2) leads to the Turaev-Vivo invariants of 3-manifolds, with the Elliott-Biedenharn identity corresponding to an Alexander move on a triangulation of a 3-manifold and the orthogonality condition corresponding to a Matveev move on the dual 2-skeleton of a... read more

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