An explicit formula for a star product with separation of variables

Preprint English OPEN
Karabegov, Alexander;
(2011)
  • Subject: 53D55 | Mathematics - Quantum Algebra
    arxiv: Astrophysics::Galaxy Astrophysics | Astrophysics::Earth and Planetary Astrophysics | Astrophysics::Solar and Stellar Astrophysics

For a star product with separation of variables * on a pseudo-Kaehler manifold we give a simple closed formula of the total symbol of the left star multiplication operator L_f by a given function f. The formula for the star product f * g can be immediately recovered fro... View more
  • References (12)
    12 references, page 1 of 2

    [1] 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.

    [2] Berezin, F.A.: Quantization. Math. USSR-Izv. 8 (1974), 1109-1165.

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

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

    [5] Gammelgaard, N. L.: A Universal Formula for Deformation Quantization on K¨ahler Manifolds, arXiv:1005.2094v2.

    [6] Gutt, S. and Rawnsley, J.: Natural star products on symplectic manifolds and quantum moment maps. Lett. Math. Phys. 66 (2003), 123 -139.

    [7] Karabegov, A.: Deformation quantizations with separation of variables on a K¨ahler manifold. Commun. Math. Phys. 180 (1996), no. 3, 745-755.

    [8] Karabegov, A.: Formal symplectic groupoid of a deformation quantization. Commun. Math. Phys. 258 (2005), 223-256.

    [9] Kontsevich, M.: Deformation quantization of Poisson manifolds, I. Lett. Math. Phys. 66 (2003), 157 - 216.

    [10] Neumaier, N.: Universality of Fedosov's construction for star-products of Wick type on pseudo-K¨ahler manifolds. Rep. Math. Phys. 52 (2003), no.1, 43-80.

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