Deformations of the algebra of functions of a symplectic manifold. Comparison between Fedosov and de Wilde, Lecomte. (Déformations de l’algèbre des fonctions d’une variété symplectique: Comparaison entre Fedosov et De Wilde, Lecomte.) (French) Zbl 0852.58033

Deligne, P.

Sel. Math., New Ser. 1, No. 4, 667-697 (1995).

M. de Wilde and P. B. A. Lecomte in their papers in Ann. Inst. Fourier 35, No. 2, 117-143 (1985; Zbl 0526.58023), Lett. Math. Phys. 7, 487-496 (1983; Zbl 0566.58039) and B. V. Fedosov in his paper “Formal quantization” [Some topics of Modern Mathematics and their applications to problems of mathematical physics, Moscow, 129-136 (1985)] have proved that if \(M\) is a symplectic manifold, then there exists a deformation \(*_t\) of the product giving place to the symplectic Poisson brackets. The classifications of the classes of isomorphy of the above deformations \(*_t\) are given by Fedosov and also by De Wilde and Lecomte.
The purpose of the present paper is to compare the applied methods, the corresponding classifications and also to explain the effect of a change of formal parameter \(t \to \sum^\infty_1 a_nt^n\) with \(a_1\) invertible.

Reviewer: N.Papaghiuc (Iaşi)

MSC:

53D55	Deformation quantization, star products
53D05	Symplectic manifolds (general theory)
53D17	Poisson manifolds; Poisson groupoids and algebroids

Keywords:

symplectic manifold; deformation; symplectic Poisson brackets

Citations:

Zbl 0566.58039; Zbl 0526.58023

References:

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