Abelian BF theories and knot invariants

Communications in Mathematical Physics

Volumn 189, Issue 3, 1997, Pages 795-828

  Cattaneo, Alberto S ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031549894     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050229     Document Type: Article

References (44)

1. Alexander, J.W.: Topological Invariants of Knots and Links. Trans. Am. Math. Soc. 30, 275-306 (1928); Conway, J.H.: An Enumeration of Knots and Links, and Some of Their Algebraic Properties. In: Computational Problems in Abstract Algebra, edited by J. Leech, New York: Pergamon Press, 1970, pp. 329-358
2. Alexander, J.W.: Topological Invariants of Knots and Links. Trans. Am. Math. Soc. 30, 275-306 (1928); Conway, J.H.: An Enumeration of Knots and Links, and Some of Their Algebraic Properties. In: Computational Problems in Abstract Algebra, edited by J. Leech, New York: Pergamon Press, 1970, pp. 329-358
3. Alfaro, J. and Damgard, P.M.: Origin of Antifields in the Batalin-Vilkovisky Lagrangian Formalism. Nucl. Phys. B 404, 751-793 (1993)
4. Anselmi, D.: Removal of Divergences with the Batalin-Vilkovisky Formalism. Class. Quant. Grav. 11 2181-2204 (1994); More on the Subtraction Algorithm. Class. Quant. Grav. 12, 319-350 (1995)
5. Anselmi, D.: Removal of Divergences with the Batalin-Vilkovisky Formalism. Class. Quant. Grav. 11 2181-2204 (1994); More on the Subtraction Algorithm. Class. Quant. Grav. 12, 319-350 (1995)
6. Bar-Natan, D.: Perturbative Aspects of the Chern-Simons Field Theory. Ph. D. Thesis, Princeton University, 1991; Perturbative Chern-Simons Theory. J. of Knot Theory and its Ramifications 4, 503-548 (1995)
7. Bar-Natan, D.: Perturbative Aspects of the Chern-Simons Field Theory. Ph. D. Thesis, Princeton University, 1991; Perturbative Chern-Simons Theory. J. of Knot Theory and its Ramifications 4, 503-548 (1995)
8. Bar-Natan, D.and Garoufalidis, S.: On the Melvin-Morton-Rozansky Conjecture. Harvard University preprint, 1994 (available at ftp://ftp.ma.huji.ac.il/drorbn)
9. Batalin, I.A. and Vilkovisky, G.A.: Relativistic S-Matrix of Dynamical Systems with Boson and Fermion Constraints. Phys. Lett. 69 B, 309-312 (1977); Fradkin, E.S. and Fradkina, T.E.: Quantization of Relativistic Systems with Boson and Fermion First-and Second-Class Constraints. Phys. Lett. 72 B, 343-348 (1978)
10. Batalin, I.A. and Vilkovisky, G.A.: Relativistic S-Matrix of Dynamical Systems with Boson and Fermion Constraints. Phys. Lett. 69 B, 309-312 (1977); Fradkin, E.S. and Fradkina, T.E.: Quantization of Relativistic Systems with Boson and Fermion First-and Second-Class Constraints. Phys. Lett. 72 B, 343-348 (1978)
11. Becchi, C., Rouet, A. and Stora, R.: Renormalization of the Abelian Higgs-Kibble Model. Commun. Math. Phys. 42, 127 (1975); Tyutin, I.V.: Lebedev Institute preprint N39, 1975
12. Becchi, C., Rouet, A. and Stora, R.: Renormalization of the Abelian Higgs-Kibble Model. Commun. Math. Phys. 42, 127 (1975); Tyutin, I.V.: Lebedev Institute preprint N39, 1975
13. Blau, M. and Thompson, G.: Topological Gauge Theories of Antisymmetric Tensor Fields. Ann. Phys. 205, 130-172 (1991)
14. Bott, R.: Configuration Spaces and Imbedding Invariants. Turkish J. of Math. 20, 1-17 (1996)
15. Bott, R. and Taubes, C.: On the Self-Linking of Knots. J. Math. Phys. 35, 5247-5287 (1994)
16. Cattaneo, A.S.: Teorie topologiche di tipo BF ed invarianti dei nodi. Ph. D. Thesis, Milan University, 1995 (available at ftp://pctheor.uni.mi.astro.it/pub/tesi.ps)
17. Cattaneo, A.S.: Cabled Wilson Loops in BF Theories. J. Math. Phys. 37, 3684-3703 (1996)
18. Cattaneo, A.S., Cotta-Ramusino, P., Fröhlich, J. and Martellini, M.: Topological BF Theories in 3 and 4 Dimensions. J. Math. Phys. 36, 6137-6160 (1995)
19. Cattaneo, A.S., Cotta-Ramusino, P. and Martellini, M.: Three-Dimensional BF Theories and the Alexander-Conway Invariant of Knots. Nucl. Phys. B 436, 355-382 (1995)
20. Cheeger, J.: Analytic Torsion and the Heat Equation. Ann. Math. 109, 259-322 (1979); Müller, W.: Analytic Torsion and the R-Torsion of Riemannian Manifolds. Adv. Math. 28, 233-305 (1978)
21. Cheeger, J.: Analytic Torsion and the Heat Equation. Ann. Math. 109, 259-322 (1979); Müller, W.: Analytic Torsion and the R-Torsion of Riemannian Manifolds. Adv. Math. 28, 233-305 (1978)
22. Cotta-Ramusino, P. and Martellini, M.: BF-Theories and 2-Knots. In Knots and Quantum Gravity. edited by J. Baez, Oxford NY: Oxford University Press, 1994, hep-th/9407097
23. Freyd, P., Yetter, D., Hoste, J., Lickorish, W.B.R., Millett, K. and Ocneanu, A.: A New Polynomial Invariant of Knots and Links. Bull. Am. Math. Soc. 12, 239-246 (1985)
24. Fröhlich, J., Götschmann, R. and Marchetti, P.A.: Bosonization of Fermi Systems in Arbitrary Dimensions in Terms of Gauge Forms. J. Phys. A 28, 1169-1204 (1995); The Effective Gauge Field Action of a System of Non-Relativistic Electrons. Commun. Math. Phys. 173, 417-452 (1995)
25. Fröhlich, J., Götschmann, R. and Marchetti, P.A.: Bosonization of Fermi Systems in Arbitrary Dimensions in Terms of Gauge Forms. J. Phys. A 28, 1169-1204 (1995); The Effective Gauge Field Action of a System of Non-Relativistic Electrons. Commun. Math. Phys. 173, 417-452 (1995)
26. Fröhlich, J. and King, C.: The Chern-Simons Theory and Knot Polynomials. Commun. Math. Phys. 126, 167-199 (1989)
27. Fulton, W. and MacPherson, R.: Compactification of Configuration Spaces. Ann. Math. 139, 183-225 (1994)
28. Guadagnini, E., Martellini, M. and Mintchev, M.: Chern-Simons Model and New Relations between the HOMFLY Coefficients. Phys. Lett. B 228, 489-494 (1989)
29. Jones, V.F.R.: A Polynomial Invariant for Knots via von Neumann Algebras. Bull. Am. Math. Soc. 12, 103-112 (1985)
30. Longoni, R.: Sviluppo perturbativo delle teorie di campo topologiche di tipo BF e invarianti dei nodi. Laurea Thesis, Milan University, 1996
31. Maggiore, N. and Sorella, S.P.: Finiteness of the Topological Models in the Landau Gauge. Nucl. Phys. B 377, 236-251 (1992)
32. Melvin, P.M. and Morton, H.R.: The Coloured Jones Function. Commun. Math. Phys. 169, 501-520 (1995)
33. Milnor, J.: A Duality Theorem for Reidemeister Torsion. Ann. Math. 76, 137-147 (1962); Turaev, V.G.: Reidemeister Torsion in Knot Theory. Russ. Math. Surveys 41, 97-147 (1986)
34. Milnor, J.: A Duality Theorem for Reidemeister Torsion. Ann. Math. 76, 137-147 (1962); Turaev, V.G.: Reidemeister Torsion in Knot Theory. Russ. Math. Surveys 41, 97-147 (1986)
35. Rozansky, L.: A Contribution of the Trivial Connection to Jones Polynomial and Witten's Invariants of 3d Manifolds. I. Commun. Math. Phys. 175, 275-296 (1996); A Contribution of the Trivial Connection to Jones Polynomial and Witten's Invariants of 3d Manifolds. II. Commun. Math. Phys. 175, 297-318 (1996)
36. Rozansky, L.: A Contribution of the Trivial Connection to Jones Polynomial and Witten's Invariants of 3d Manifolds. I. Commun. Math. Phys. 175, 275-296 (1996); A Contribution of the Trivial Connection to Jones Polynomial and Witten's Invariants of 3d Manifolds. II. Commun. Math. Phys. 175, 297-318 (1996)
37. Schwarz, A.: Geometry of Batalin-Vilkovisky Quantization. Commun. Math. Phys. 155, 249-260 (1993); Alexandrov, M., Kontsevich, M., Schwarz, A. and Zaboronsky, O.: The Geometry of the Master Equation and Topological Quantum Field Theory. hep-th/9502010
38. Schwarz, A.: Geometry of Batalin-Vilkovisky Quantization. Commun. Math. Phys. 155, 249-260 (1993); Alexandrov, M., Kontsevich, M., Schwarz, A. and Zaboronsky, O.: The Geometry of the Master Equation and Topological Quantum Field Theory. hep-th/9502010
39. Schwarz, A.S.; The Partition Function of Degenerate Quadratic Functionals and Ray-Singer Invariants. Lett. Math. Phys. 2, 247-252 (1978)
40. Voronov, B.L. and Tyutin, I.V.: Formulation of Gauge Theories of General Form. I. Theor. Math. Phys. 50, 218-225 (1982); Batalin, I.A. and Vilkovisky, G.A.: Existence Theorem for Gauge Algebra. J. Math. Phys. 26, 172-184 (1985); Fisch, J.M.L. and Henneaux, M.: Homological Perturbation Theory and the Algebraic Structure of the Antifield-Antibracket Formalism for Gauge Theories. Commun. Math. Phys. 128, 627-640 (1990)
41. Voronov, B.L. and Tyutin, I.V.: Formulation of Gauge Theories of General Form. I. Theor. Math. Phys. 50, 218-225 (1982); Batalin, I.A. and Vilkovisky, G.A.: Existence Theorem for Gauge Algebra. J. Math. Phys. 26, 172-184 (1985); Fisch, J.M.L. and Henneaux, M.: Homological Perturbation Theory and the Algebraic Structure of the Antifield-Antibracket Formalism for Gauge Theories. Commun. Math. Phys. 128, 627-640 (1990)
42. Voronov, B.L. and Tyutin, I.V.: Formulation of Gauge Theories of General Form. I. Theor. Math. Phys. 50, 218-225 (1982); Batalin, I.A. and Vilkovisky, G.A.: Existence Theorem for Gauge Algebra. J. Math. Phys. 26, 172-184 (1985); Fisch, J.M.L. and Henneaux, M.: Homological Perturbation Theory and the Algebraic Structure of the Antifield-Antibracket Formalism for Gauge Theories. Commun. Math. Phys. 128, 627-640 (1990)
43. Witten, E.: Quantum Field Theory and the Jones Polynomial. Commun. Math. Phys. 121, 351-399 (1989)
44. Witten, E.: A Note on the Antibracket Formalism. Mod. Phys. Lett. A 5, 487-494 (1990)