A Fedosov Star Product of Wick Type for Kähler Manifolds

Details A Fedosov Star Product of Wick Type for Kähler Manifolds A Fedosov Star Product of Wick Type for Kähler Manifolds

1996-05-08

arxiv.org/abs/q-alg/9605012v1

Mathematics

Quantum Algebra

10 pages, LaTeX2e

Scientific paper

In this letter we compute some elementary properties of the Fedosov star product of Weyl type, such as symmetry and order of differentiation. Moreover, we define the notion of a star product of Wick type on every K\"ahler manifold by a straight forward generalization of the corresponding star product in $\mathbb C^n$: the corresponding sequence of bidifferential operators differentiates its first argument in holomorphic directions and its second argument in antiholomorphic directions. By a Fedosov type procedure we give an existence proof of such star products for any K\"ahler manifold.

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