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1998 | 42 | 1 | 187-204
Tytuł artykułu

Spin networks and the bracket polynomial

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper discusses Penrose spin networks in relation to the bracket polynomial.
Słowa kluczowe
Rocznik
Tom
42
Numer
1
Strony
187-204
Opis fizyczny
Daty
wydano
1998
Twórcy
  • Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, Illinois 60607-7045, U.S.A.
Bibliografia
  • [1] D. Bullock, Rings of $SL_2(C)$ characters and the Kauffman bracket skein module, preprint, 1996.
  • [2] J. Scott Carter, D. E. Flath and M. Saito, The Classical and Quantum 6j-Symbols, Math. Notes 43, Princeton Univ. Press, 1995.
  • [3] J. Scott Carter, L. H. Kauffman and M. Saito, Diagrammatics, Singularities and Their Algebraic Interpretations, in: Conference Proceedings of the Brasilian Mathematical Society, to appear.
  • [4] L. Crane and I. Frenkel, Four dimensional topological quantum field theory, Hopf categories and canonical bases, J. Math. Phys. 35 (1994), 5136-5154.
  • [5] L. Crane, L. H. Kauffman and D. Yetter, State sum invariants of 4-manifolds, J. Knot Theory and Its Ramifications, 1997, to appear.
  • [6] D. S. Freed and R. E. Gompf, Computer calculation of Witten's three-manifold invariant, Comm. Math. Phys. 141 (1991), 79-117.
  • [7] B. Hasslacher and M. J. Perry, Spin networks are simplicial quantum gravity, Phys. Lett. B 103 (1981), 21-24.
  • [8] L. C. Jeffrey, Chern-Simons-Witten invariants of lens spaces and torus bundles, and the semi-classical approximation, Comm. Math. Phys. 147 (1992), 563-604.
  • [9] V. F. R. Jones, A polynomial invariant of links via von Neumann algebras, Bull. Amer. Math. Soc. 129 (1985), 103-112.
  • [10] L. H. Kauffman, State models and the Jones polynomial, Topology 26 (1987), 395-407.
  • [11] L. H. Kauffman, Statistical mechanics and the Jones polynomial, in: Contemp. Math. 78, Amer. math. Soc., 1989, 263-297.
  • [12] L. H. Kauffman, Map coloring, q-deformed spin networks, and Turaev-Viro invariants for 3-manifolds, Internat. J. Modern Phys. B 6 (1992), 1765-1794.
  • [13] L. H. Kauffman, Knots and Physics, World Scientific, 1991, 1993.
  • [14] L. H. Kauffman and S. L. Lins, Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds, Ann. Math. Stud. 114, Princeton Univ. Press, 1994.
  • [15] R. Lawrence, Asymptotic expansions of Witten-Reshetikhin-Turaev invariants for some simple 3-manifolds, J. Math. Phys. 36 (1995), 6106-6129.
  • [16] J. P. Moussouris, Quantum Models of Space-Time Based on Recoupling Theory, thesis, Oxford Univ., 1983.
  • [17] R. Penrose, Angular momentum: An approach to Combinatorial Spacetime, in: Quantum Theory and Beyond, T. Bastin (ed.), Cambridge Univ. Press, 1969.
  • [18] R. Penrose, Applications of negative dimensional tensors, in: Combinatorial Mathematics and Its Applications, D. J. A. Welsh (ed.), Academic Press, 1971.
  • [19] G. Ponzano and T. Regge, Semiclassical limit of Racah coefficients, in: Spectroscopic and Group Theoretical Methods in Theoretical Physics, North-Holland, Amsterdam, 1968.
  • [20] K. Reidemeister, Knotentheorie, Julius Springer, Berlin, 1933; Chelsea, N.Y., 1948.
  • [21] N. Y. Reshetikhin and V. Turaev, Invariants of Three Manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), 547-597.
  • [22] L. Rozansky, Witten's invariant of 3-dimensional manifolds: loop expansion and surgery calculus, in: Knots and Applications, L. Kauffman (ed.), World Scientific, 1995.
  • [23] A. Schwarz, The partition function of degenerate quadratic functional and Ray-Singer invariants, Lett. Math. Phys. 2 (1978), 247.
  • [24] L. Smolin, The geometry of quantum spin networks, preprint, Center for Gravitational Physics and Geometry, Penn. State University, University Park, PA, 1996.
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  • [26] E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), 351-399.
  • [27] E. Witten, 2+1 gravity as an exactly soluble system, Nuclear Phys. B 311, (1988/89), 46-78.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv42i1p187bwm
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