Four-dimensional lattice gauge theory with ribbon categories and the Crane-Yetter state sum

Journal of Mathematical Physics

Volumn 42, Issue 11, 2001, Pages 5272-5305

  Pfeiffer, Hendryk ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035605404     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1398063     Document Type: Article

References (29)

1. K. G. Wilson, "Confinement of Quarks," Phys. Rev. D 10(8), 2445-2459 (1974).
2. D. V. Boulatov, "q-deformed lattice gauge theory and 3-manifold invariants," Int. J. Mod. Phys. A 8(18), 3139-3162 (1993), hep-th/9210032.
3. R. Oeckl, "Lattice gauge theory, spin foams and quantum groups," in preparation (2001).
4. R. Dijkgraaf and E. Witten, "Topological gauge theories and group cohomology," Commun. Math. Phys. 129, 393-429 (1990).
5. M. Wakui, "On Dijkgraaf-Witten invariant for 3-manifolds," Osaka J. Math. 29(4), 675-696 (1992).
6. V. G. Turaev and O. Y. Viro, "State sum invariants of 3-manifolds and quantum 6j-symbols," Topology 31(4), 865-902 (1992).
7. J. W. Barrett and B. W. Westbury, "Invariants of piecewise-linear 3-manifolds," Trans. Am. Math. Soc. 348(10), 3997-4022 (1996), hep-th/9311155.
8. J. C. Baez, "An introduction to spin foam models of BF theory and quantum gravity," in Geometry and Quantum Physics, Lecture Notes in Physics Vol. 543 (Springer, Berlin, 2000), pp. 25-93, gr-qc/9905087.
9. L. Crane and D. N. Yetter, "A categorical construction of 4d topological QFT," in Quantum Topology, Series on Knots and Everything 3 (World Scientific, Singapore, 1993), pp. 12-130, hep-th/9301062.
10. L. Crane, L. H. Kauffmann, and D. N. Yetter, "State-sum invariants of 4-manifolds," J. Knot Th. Ramif. 6(2), 177-234 (1997), hep-th/9409167.
11. M. P. Reisenberger and C. Rovelli, "'Sum over surfaces' form of loop quantum gravity," Phys. Rev. D 56, 3490-3508 (1997), gr-qc/9612035.
12. J. C. Baez, "Spin foam models," Class. Quantum Grav. 15(7), 1827-1858 (1998), gr-qc/9709052.
13. H. Ooguri, "Topological lattice models in four dimensions," Mod. Phys. Lett. A 7(30), 2799-2810 (1992).
14. J. W. Barrett and L. Crane, "Relativistic spin networks and quantum gravity," J. Math. Phys. 39, 3296-3302 (1998), gr-qc/9709028.
15. I. Montvay and G. Münster, Quantum Fields on a Lattice (Cambridge U.P., Cambridge, 1994).
16. H. J. Rothe, Lattice Gauge Theories - An Introduction (World Scientific, Singapore, 1992).
17. R. Oeckl and H. Pfeiffer, "The dual of pure non-Abelian lattice gauge theory as a spin foam model," Nucl. Phys. B 598(1-2), 400-426 (2001), hep-th/0008095.
18. M. E. Peskin, "Mandelstam-t'Hooft Duality in Abelian Lattice Models," Ann. Phys. 113, 122-152 (1978).
19. R. Savit, "Duality in field theory and statistical systems," Rev. Mod. Phys. 52(2), 453-487 (1980).
20. R. Anishetty, S. Cheluvaraja, H. S. Sharatchandra, and M. Mathur, "Dual of 3-dimensional pure SU(2) lattice gauge theory and the Ponzano-Regge model," Phys. Lett. B 314, 387-390 (1993), hep-lat/9210024.
21. V. Chari and A. Pressley, A Guide to Quantum Groups (Cambridge U.P., Cambridge, 1994).
22. S. Majid, Foundations of Quantum Group Theory (Cambridge U.P., Cambridge, 1995).
23. N. Reshetikhin and V. G. Turaev, "Ribbon graphs and their invariants derived from quantum groups," Commun. Math. Phys. 127, 1-26 (1990).
24. T. Bröcker and T. Dieck, Representations of Compact Lie Groups, Graduate Texts in Mathematics 98 (Springer, New York, 1985).
25. R. Carter, G. Segal, and I. Macdonald, Lectures on Lie Groups and Lie Algebras, London Mathematical Society Student Texts 32 (Cambridge U.P., Cambridge, 1995).
26. V. G. Turaev, Quantum Invariants of Knots and 3-manifolds (de Gruyter, Berlin, 1994).
27. S. MacLane, Categories for the Working Mathematician, Graduate Texts in Mathematics (Springer, Berlin, 1973).
28. D. V. Boulatov, "Quantun deformation of lattice gauge theory," Commun. Math. Phys. 186, 295-322 (1997), hep-th/9604117.
29. G. Carbone, M. Carfora, and A. Marzuoli, "Hierarchies of invariant spin models," Nucl. Phys. B 595(3), 654-688 (2001), gr-qc/0008011.