Volume 17, issue 1 (2013)

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Asymptotics of classical spin networks

Stavros Garoufalidis and Roland van der Veen

Appendix: Don Zagier

Geometry & Topology 17 (2013) 1–37
Bibliography
1 A Abdesselam, On the volume conjecture for classical spin networks arXiv:1009.2811
2 C C Adams, The knot book, W. H. Freeman and Co. (1994) MR1266837
3 Y André, Séries Gevrey de type arithmétique, I, Théorèmes de pureté et de dualité, Ann. of Math. 151 (2000) 705 MR1765707
4 V Aquilanti, H M Haggard, A Hedeman, N Jeevanjee, R G Littlejohn, L Yu, Semiclassical mechanics of the Wigner 6j–Symbol arXiv:0904.1734
5 C M Bender, S A Orszag, Advanced mathematical methods for scientists and engineers, I Asymptotic methods and perturbation theory, Springer (1999) MR1721985
6 L C Biedenharn, J D Louck, Angular momentum in quantum physics, 8, Addison-Wesley Publishing Co. (1981) MR635121
7 L C Biedenharn, J D Louck, The Racah–Wigner algebra in quantum theory, 9, Addison-Wesley Publishing Co. (1981) MR636504
8 S Bloch, D Kreimer, Mixed Hodge structures and renormalization in physics, Commun. Number Theory Phys. 2 (2008) 637 MR2492196
9 L M Blumenthal, Theory and applications of distance geometry, , Chelsea Publishing Co. (1970) MR0268781
10 J S Carter, D E Flath, M Saito, The classical and quantum 6j–symbols, 43, Princeton Univ. Press (1995) MR1366832
11 F Costantino, Integrality of Kauffman brackets of trivalent graphs arXiv:0908.0542
12 F Costantino, J Marché, Generating series and asymptotics of classical spin networks arXiv:1103.5644
13 M Dupuis, E R Livine, Pushing the asymptotics of the 6j–symbol further, Phys. Rev. D 80 (2009) 024035 MR2570033
14 J Engle, R Pereira, C Rovelli, Flipped spinfoam vertex and loop gravity, Nuclear Phys. B 798 (2008) 251 MR2413668
15 S Garoufalidis, Applications of quantum invariants in low-dimensional topology, Topology 37 (1998) 219 MR1480887
16 S Garoufalidis, G-functions and multisum versus holonomic sequences, Adv. Math. 220 (2009) 1945 MR2493185
17 S Garoufalidis, What is a sequence of Nilsson type ?, from: "Interactions between hyperbolic geometry, quantum topology and number theory" (editors A Champanerkar, O Dasbach, E Kalfagianni, I Kofman, W Neumann, N Stoltzfus), Contemp. Math. 541, Amer. Math. Soc. (2011) 145
18 S Garoufalidis, A Its, A Kapaev, M Mariño, Asymptotics of the instantons of Painlevé I arXiv:1002.3634
19 S Garoufalidis, M Mariño, Universality and asymptotics of graph counting problems in non-orientable surfaces, J. Combin. Theory Ser. A 117 (2010) 715 MR2645187
20 S Garoufalidis, R van der Veen, Asymptotics of quantum spin networks at a fixed root of unity, Math. Ann. (2011) 1 MR2892459
21 D B Grünberg, P Moree, Sequences of enumerative geometry: congruences and asymptotics, Experiment. Math. 17 (2008) 409 MR2484425
22 H M Haggard, R G Littlejohn, Asymptotics of the Wigner 9j–symbol, Classical and Quantum Gravity 27 (2010) 135010 MR2654048
23 V F R Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. 126 (1987) 335 MR908150
24 R Kashaev, The hyperbolic volume of knots from the quantum dilogarithm, Lett. Math. Phys 39 (1997) 296 MR1434238
25 M Kauers, Mathematica, Software
26 M Kauers, Guessing Handbook, RISC Report Series, Johannes Kepler University Linz, Austria, 09-07 (2009)
27 L H Kauffman, S L Lins, Temperley–Lieb recoupling theory and invariants of 3–manifolds, 134, Princeton Univ. Press (1994) MR1280463
28 A N Kirillov, N Y Reshetikhin, Representations of the algebra Uq(sl(2)),q-orthogonal polynomials and invariants of links, from: "Infinite-dimensional Lie algebras and groups" (editor V G Kac), Adv. Ser. Math. Phys. 7, World Sci. Publ., Teaneck, NJ (1989) 285 MR1026957
29 R G Littlejohn, L Yu, Semiclassical Analysis of the Wigner 9J–Symbol with Small and Large Angular Momenta, To appear in Phys. Rev. A arXiv:1104.1499
30 P D Miller, Applied asymptotic analysis, 75, Amer. Math. Soc. (2006) MR2238098
31 J P Moussouris, The chromatic evaluation of strand networks, from: "Advances in Twistor Theory" (editors L P Huston, R S Ward), Research Notes in Mathematics 37, Pitman (1979) 308 MR578487
32 J Murakami, H Murakami, The colored Jones polynomials and the simplicial volume of a knot, Acta Math. 186 (2001) 85 MR1828373
33 F W J Olver, Asymptotics and special functions, , A K Peters Ltd. (1997) MR1429619
34 P Paule, A Riese, qZeil, Mathematica Software
35 R Penrose, Angular Momentum: An approach to combinatorial space time, from: "Quantum Theory and Beyond" (editor T Bastin), Research Notes in Mathematics, Cambridge Univ. Press (1971) 151
36 R Penrose, Applications of negative dimensional tensors, from: "Combinatorial Mathematics and its Applications, Proc. Conf.", Academic Press (1971) 221 MR0281657
37 G Ponzano, T Regge, Semiclassical limit of Racah coefficients, from: "Spectroscopic and group theoretical methods in physics", Research Notes in Mathematics, North Holland (1968) 1
38 G Racah, Theory of complex spectra I, Physical Rev. 61 (1946) 186 MR0018576
39 G Racah, Theory of complex spectra II, Physical Rev. 61 (1942) 186 MR0018576
40 G Racah, Theory of complex spectra III, Physical Rev. 62 (1942) 438 MR0018576
41 G Racah, Theory of complex spectra IV, Physical Rev. 76 (1949) 1352 MR0018576
42 J Roberts, Classical 6j–symbols and the tetrahedron, Geom. Topol. 3 (1999) 21 MR1673272
43 J Roberts, Asymptotics and 6j-symbols, from: "Invariants of knots and 3–manifolds", Geom. Topol. Monogr. 4, Geom. Topol. Publ., Coventry (2002) 245 MR2002614
44 C Rovelli, L Smolin, Discreteness of area and volume in quantum gravity, Nuclear Phys. B 442 (1995) 593 MR1332705
45 C L Siegel, Über einige Anwendungen diophantischer Approximationen, Abh. Preuss. Akad. Wiss. (1929)
46 V G Turaev, Quantum invariants of knots and 3–manifolds, 18, Walter de Gruyter & Co. (1994) MR1292673
47 V G Turaev, O Y Viro, State sum invariants of 3–manifolds and quantum 6j–symbols, Topology 31 (1992) 865 MR1191386
48 D A Varshalovich, A N Moskalev, V K Khersonskiĭ, Quantum theory of angular momentum, World Scientific Publishing Co. (1988) MR1022665
49 W Wasow, Asymptotic expansions for ordinary differential equations, Dover Publications (1987) MR919406
50 B W Westbury, A generating function for spin network evaluations, from: "Knot theory" (editors V F R Jones, J Kania-Bartoszyńska, J H Przytycki, P Traczyk, V G Turaev), Banach Center Publ. 42, Polish Acad. Sci. (1998) 447 MR1634471
51 H Whitney, 2–Isomorphic Graphs, Amer. J. Math. 55 (1933) 245 MR1506961
52 E P Wigner, On representations of certain finite groups, Amer. J. Math. 63 (1941) 57 MR0003417
53 J Wimp, D Zeilberger, Resurrecting the asymptotics of linear recurrences, J. Math. Anal. Appl. 111 (1985) 162 MR808671
54 D Zagier, Vassiliev invariants and a strange identity related to the Dedekind eta-function, Topology 40 (2001) 945 MR1860536