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Asymptotics of classical
spin networks
Stavros Garoufalidis and Roland van der VeenAppendix: Don Zagier |
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Geometry & Topology 17 (2013) 1–37
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DOI: 10.2140/gt.2013.17.1
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Abstract |
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A spin network is a cubic ribbon graph labeled by representations of . Spin networks are important in various areas of Mathematics (–dimensional Quantum Topology), Physics (Angular Momentum, Classical and Quantum Gravity) and Chemistry (Atomic Spectroscopy). The evaluation of a spin network is an integer number. The main results of our paper are: (a) an existence theorem for the asymptotics of evaluations of arbitrary spin networks (using the theory of –functions), (b) a rationality property of the generating series of all evaluations with a fixed underlying graph (using the combinatorics of the chromatic evaluation of a spin network), (c) rigorous effective computations of our results for some –symbols using the Wilf–Zeilberger theory and (d) a complete analysis of the regular Cube spin network (including a nonrigorous guess of its Stokes constants), in the appendix. |
Keywords
Spin networks, ribbon graphs, $6j$–symbols, Racah
coefficients, angular momentum, asymptotics, G-functions,
Kauffman bracket, Jones polynomial, Wilf-Zeilberger method,
Borel transform, enumerative combinatorics, recoupling,
Nilsson
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Mathematical Subject Classification 2010
Primary: 57N10
Secondary: 57M25
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References |
Publication
Received: 20 February 2009
Revised: 9 May 2012
Accepted: 12 July 2012
Published: 5 February 2013
Proposed: Walter Neumann
Seconded: Vaughan Jones, Yasha Eliashberg
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Authors |
| Stavros Garoufalidis | |
| School of Mathematics Georgia Institute of Technology 686 Cherry Street Atlanta, GA 30332-0160 USA |
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| http://www.math.gatech.edu/~stavros | |
| Roland van der Veen | |
| Department of Mathematics University of California Berkeley, CA 94720-3840 USA |
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| http://www.math.berkeley.edu/~roland | |
| Don Zagier | |
| Max Planck Institute for
Mathematics Vivatsgasse 7, 53111 Bonn Germany |
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| http://people.mpim-bonn.mpg.de/zagier/ | |
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