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arXiv:math-ph/0208028 · Journal of Physics A Mathematical and General

Weyl-Underhill-Emmrich quantization and the Stratonovich-Weyl quantizer

Jerzy F Plebanski, Maciej Przanowski, Francisco J. Turrubiates

Published Jan 24, 2000• 3 citations
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Abstract

Weyl-Underhill-Emmrich (WUE) quantization and its generalization are considered. It is shown that an axiomatic definition of the Stratonovich-Weyl quantizer leads to severe difficulties. Quantization on the cylinder within the WUE formalism is discussed.
DOI
10.1088/0305-4470/33/4/312

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The Stratonovich–Weyl correspondence is a restatement of the Moyal quantization where the phase space is a manifold and where a group of transformations acts on it transitively. The first and most important step is to define a mapping from the manifold into the set of self-adjoint operators on a Hilbert space, under suitable conditions. This mapping is called a Stratonovich–Weyl kernel. The construction of this mapping is discussed on coadjoint orbits of the one-dimensional Galilei, Poincaré, and Newton–Hooke groups as well as the two-dimensional Euclidean group.