Homogeneous Fedosov star products on cotangent bundles. I: Weyl and standard ordering with differential operator representation. (English) Zbl 0968.53056

Bordemann, Martin; Neumaier, Nikolai; Waldmann, Stefan

Commun. Math. Phys. 198, No. 2, 363-396 (1998).

The authors deal with the construction of homogeneous star products of Weyl type on every cotangent bundle \(T^*Q\) by means of the Fedosov procedure using a symplectic torsion-free connection on \(T^*Q\) which is homogeneous of degree zero with respect to the Liouville vector field. The main motivation for the authors was to apply the formal GNS construction in deformation quantization to the particular case of \(T^*Q\). Motivated by the flat case \(T^*\mathbb{R}^N\) another homogeneous star product of Weyl type corresponding to the Weyl ordering prescription is constructed.

Reviewer: Messoud Efendiev (Berlin)

MSC:

53D55	Deformation quantization, star products
37J05	Relations of dynamical systems with symplectic geometry and topology (MSC2010)
53D50	Geometric quantization

Keywords:

homogeneous star product; Fedosov procedure; Liouville vector field; quantization