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VOL. 22 | 2021 Star Product on The Euclidean Motion Group in the Plane
Laarni B. Natividad, Job A. Nable

Editor(s) Ivaïlo M. Mladenov, Vladimir Pulov, Akira Yoshioka

Abstract

In this work, we perform exact and concrete computations of star-product of functions on the Euclidean motion group in the plane, and list its $C$-star- algebra properties. The star-product of phase space functions is one of the main ingredients in phase space quantum mechanics, which includes Weyl quantization and the Wigner transform, and their generalizations. These methods have also found extensive use in signal and image analysis. Thus, the computations we provide here should prove very useful for phase space models where the Euclidean motion groups play the crucial role, for instance, in quantum optics.

Information

Published: 1 January 2021
First available in Project Euclid: 2 June 2021

Digital Object Identifier: giq-22-2021-199-208

Rights: Copyright © 2021 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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