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[Licence| Download | New Version Template] aebu_v2_0.tar.gz(41 Kbytes)
Manuscript Title: The Fedosov *-product in Mathematica
Authors: Jaromir Tosiek
Program title: Fecom.nb
Catalogue identifier: AEBU_v2_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 181(2010)704
Programming language: Mathematica v.6.0.
Computer: All.
Operating system: All.
RAM: Sufficient for installation of Mathematica
Keywords: Deformation quantization, Fedosov formalism.
Classification: 17.16.

Does the new version supersede the previous version?: Yes

Nature of problem:
Computing the *-product of the Weyl type in the Fedosov formalism in a Darboux chart

Solution method:
Inputting the dimension of the phase space, coeiffcients of the symplectic connection, the range of approximation and the functions to be multiplied; computing the Abelian connection and the flat sections of the Weyl bundle representing the multiplied functions; calculating the projection of the o- product of these flat sections on the phase space.

Reasons for new version:
Optimization and including the trivial cases - deformations of the 0th and the 1st order.

Summary of revisions:
In case we calculate the *-product up to the odd power hk, it is necessary to know the Abelian connection and the flat sections up to the degree 2k - 1. But for the even power hk, it is sufficient to know the Abelian connection and the flat sections up to the degree 2k - 2. In the new version of the program we use this observation. Now the running time of the program for even powers hk is shorter than in the previous version.
The 0th and the 1st order of the deformation are trivial - the pointwise product of functions and the Poisson bracket of them respectively. But to make the program complete we added the possibility of calculating also these trivial situations. The new version of the program works then also for the maximal power of h equal 0 and 1 ħ.

Running time:
The test run, provided with the distribution, took approximately 2 minutes to run using Mathematica 7.0 on a Windows XP machine.