A heat kernel proof of the index theorem for deformation quantization

Preprint English OPEN
Karabegov, Alexander;
(2017)

We give a heat kernel proof of the algebraic index theorem for deformation quantization with separation of variables on a pseudo-Kahler manifold. We use normalizations of the canonical trace density of a star product and of the characteristic classes involved in the ind... View more
  • References (26)
    26 references, page 1 of 3

    [1] Alvarez-Gaum´e, L.: Supersymmetry and the Atiah-Singer index theorem. Comm. Math. Phys. 90 (1983), 161-173.

    [2] Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., and Sternheimer, D.: Deformation theory and quantization. I. Deformations of symplectic structures. Ann. Physics 111 (1978), no. 1, 61 - 110.

    [3] Berline, N., Getzler, E., and Vergne, M.: Heat Kernels and Dirac operators. (1992), Berlin: Springer-Verlag.

    [4] Bertelson, M., Cahen M., and Gutt, S.: Equivalence of star products, Class. Quan. Grav. 14 (1997), A93 - A107.

    [5] Bordemann, M.: The deformation quantization of certain super-Poisson brackets and BRST cohomology. Conf´erence Mosh´e Flato 1999. Vol. II, Kluwer, Dordrecht, (2000), 45-68.

    [6] Bordemann, M., Waldmann, S.: A Fedosov star product of the Wick type for K¨ahler manifolds. Lett. Math. Phys. 41 (3) (1997), 243 - 253.

    [7] Deligne, P.: D´eformations de l'Alg`ebre des Fonctions d'une Vari´et´e Symplectique: Comparaison entre Fedosov et De Wilde Lecomte, Selecta Math. (New series). 1 (1995), 667- 697.

    [8] Dolgushev, V. A. and Rubtsov, V. N.: An Algebraic Index Theorem for Poisson Manifolds. J. Reine Angew. Math. 633 (2009), 77 -113;

    [9] Fedosov, B.: A simple geometrical construction of deformation quantization. J. Differential Geom. 40 (1994), no. 2, 213-238.

    [10] Fedosov, B.: Deformation quantization and index theory. Mathematical Topics. Vol. 9. Akademie Verlag, Berlin (1996).

  • Metrics
Share - Bookmark