Quantum field theories on an algebraic curve

Letters in Mathematical Physics

Volumn 52, Issue 1, 2000, Pages 79-91

  Takhtajan, Leon A ^a  

^a STONY BROOK UNIVERSITY   (United States)

Author keywords

Algebraic curves; Clifford and Heisenberg algebras; Quantum field theories; Reciprocity laws; Ward identities

Indexed keywords

EID: 0039334764     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007605903393     Document Type: Article

References (29)

1. Witten, E.: Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), 351-399.
2. Donaldson, S.: The Seiberg-Witten equations and 4-manifolds topology, Bull. Amer. Math. Soc. (N. S.) 33 (1996), 45-70.
3. Witten, E.: Monopoles and four-manifolds, Math. Res. Lett. 1 (1994), 769-796.
4. Frenkel, I., Lepowsky, J., and Meurman, A.: Vertex Operator Algebras and the Monster, Academic Press, Boston, 1988.
5. Witten, E.: Two-dimensional quantum gravity and intersection theory on moduli space, Surv. Differential Geom. 1 (1991), 243-310.
6. Kontsevich, M.: Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147 (1992), 1-23.
7. Manin Yu. I. and Zograf, P.: Invertible cohomological field theories and Weil-Petersson volumes, Preprint math.AG/9902051.
8. Zograf P. and Takhtajan, L.: Action of the Liouville equation is a generating function for the accessory parameters and potential of the Weil-Petersson metric on the Teichmüller space, Funct. Anal. Appl. 19 (1985), 219-220.
9. Takhtajan, L.: Topics in quantum geometry of Riemann surfaces: two-dimensional quantum gravity, In: L. Castellani and E. Wess, (eds), Quantum Groups and their Applications in Physics (Varenna, 1994), Proc. Internat. School Phys. Enrico Fermi, 127, IOS, Amsterdam, 1996, pp. 541-579.
10. Dito, G., Flato, M., Sternheimer, D., and Takhtajan, L.: Deformation quantization and Nambu mechanics, Comm. Math. Phys. 183 (1997), 1-22.
11. Tate, J.: Residues of differentials on curves, Ann. Sci. École Norm. Sup. 1 (1968), 149-159.
12. Arbarello, E., De Concini C., and Kac, V.: The infinite wedge representation and the reciprocity law for algebraic curves, In: Theta Functions - Bowdoin 1987, Part 1 (Brunswick, ME, 1987), Proc. Sympos. Pure Math. 49, Amer. Math. Soc., Providence, RI, 1989, pp. 171-190.
13. Kazhdan, D.: Lecture on the AMS Summer Research Institute 'Theta Functions', Bowdoin College, Maine 1987 (unpublished).
14. Witten,E.: Quantum field theory, Grassmannians, and algebraic curves, Comm. Math. Phys. 113 (1988), 529-600.
15. Witten, E.: Free fermions on an algebraic curve, In: The mathematical heritage of Hermann Weyl (Durham, NC, 1987), Proc. Sympos. Pure Math. 48, Amer. Math. Soc., Providence, RI, 1988, pp. 329-344.
16. Garland, H. and Zuckerman, G.: Representations of Heisenberg systems and vertex operators, In: Complex Geometry and Lie Theory (Sundance, UT, 1989), Proc. Sympos. Pure Math. 53, Amer. Math. Soc., Providence, RI, 1991, pp. 135-150.
17. Beilinson, A., Feigin, B., and Mazur, B.: Introduction to algebraic field theory on curves, Unpublished manuscript.
18. Raina, A.: Fay's trisecant identity and conformal field theory, Comm. Math. Phys. 122 (1989), 625-641.
19. Raina, A.: An algebraic geometry study of the b - c system with arbitrary twist fields and arbitrary statistics, Comm. Math. Phys. 140 (1991), 373-397.
20. Beilinson, A. and Drinfeld, V.: Chiral algebras I., Unpublished manuscript.
21. Beilinson, A. and Drinfeld, V: Quantization of Hitchin's integrable system and Hecke eigensheaves, Unpublished manuscript.
22. Gaitsgory, D.: Notes on 2d conformal field theory and string theory. In: P. Deligne et al. (eds), Quantum Fields and Strings. A Course for Mathematicians, Amer. Math. Soc., Providence, RI, 1999, pp. 1017-1089.
23. Artin, E. and J. Tate, J.: Class Field Theory, W. A. Benjamin, New York, 1968.
24. Belavin, A., Polyakov A., and Zamolodchikov, A.: Infinite conformal symmetry in two-dimensional quantum field theory, Nuclear Phys. B 241 (1984), 333-380.
25. Iwasawa, K.: Algebraic Functions, Transl. Math. Monogr. 118, Amer. Math. Soc., Providence, RI, 1993.
26. Serre, J.-P.: Groupes algébriques et corps de classes, Hermann, Paris, 1959.
27. Serre, J.-P.: Local Fields, GTM 67, Springer-Verlag, New York, 1979.
28. Artin, E.: Algebraic Numbers and Algebraic Functions, Gordon and Breach, New York, 1967.
29. Sen, S. and Raina, A.: Grassmannians, multiplicative Ward identities and theta-function identities, Phys. Lett. B 203 (1988), 256-262.