Star products made (somewhat) easier

Details Star products made (somewhat) easier Star products made (somewhat) easier

2008-06-27

arxiv.org/abs/0806.4615v3

Eur.Phys.J.C58:627-637,2008

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, v2, v3: comments and references added

Scientific paper

10.1140/epjc/s10052-008-0804-2

We develop an approach to the deformation quantization on the real plane with an arbitrary Poisson structure which based on Weyl symmetrically ordered operator products. By using a polydifferential representation for deformed coordinates $\hat x^j$ we are able to formulate a simple and effective iterative procedure which allowed us to calculate the fourth order star product (and may be extended to the fifth order at the expense of tedious but otherwise straightforward calculations). Modulo some cohomology issues which we do not consider here, the method gives an explicit and physics-friendly description of the star products.

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