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Journals and Conferences
The computer program 'Fecom.nb' implementing the Fedosov *-product in Darboux coordinates is presented. It has been written in Mathematica 6.0 but it can be easily modified to be run in some earlier version of Mathematica. To optimize computations elements of the Weyl algebra are treated as polynomials. Several procedures which order the terms are included.
Deformation quantization of the phase space R2n was invented in the middle of the previous century. Making use of the results obtained by Weyl , Wigner  and Groenewold  Moyal  presented quantum mechanics perceived as a statistical theory. The first successful generalization of Moyal’s results in case of a phase space different from R2n appeared… (More)
General properties of Abelian connection in Fedosov deformation quantization are investigated. Criteria of being a finite series for an Abelian connection are presented. Conditions for different symplectic connections to generate the same correction to the Abelian connection are given. A proof that in 2–dimensional case the Abelian connection is an ifinite… (More)
Construction of an infinite dimensional differentiable manifold R ∞ not modelled on any Banach space is proposed. Definition, metric and differential structures of a Weyl algebra (P * p M [], •) and a Weyl algebra bundle (P * M[], •) are presented. Continuity of the •-product in the Tichonov topology is proved. Construction of the *-product of the… (More)
The Fedosov deformation quantization on a cotangent bundle with a symplectic connection induced by some Riemannian connection on a base space is considered. Construction of the symplectic connection on the cotangent determined by the Riemannian connection is proposed. A detailed analysis of an Abelian connection and flat sections representing special… (More)