Quantum Half-Planes via Deformation Quantization

Details Quantum Half-Planes via Deformation Quantization Quantum Half-Planes via Deformation Quantization

1999-05-02

arxiv.org/abs/math/9905002v2

Mathematics

Quantum Algebra

12 pages, LaTeX2e with AMS-Latex style

Scientific paper

We demonstrate the main idea of constructing irreducible unitary representations of Lie groups by using Fedosov deformation quantization in the concrete case of the group Aff(R) of affine transformations of the real straight line. By an exact computation of the star-product and the operator $\hat{\ell}_Z$, we show that the resulting representations exhausted all the irreducible representations of this groups.

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