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VOL. 22 | 2021 The Transformation of Commutative Phase Space to Noncommutative One, and Its Lorentz Transformation-Like Forms
Makoto Nakamura, Hiroshi Kakuhata, Kouichi Toda

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

Abstract

Noncommutative phase space of arbitrary dimension is discussed. We introduce momentum-momentum noncommutativity in addition to coordinate-coordinate noncommutativity. We find an exact form for the linear transformation which relates a noncommutative phase space to the corresponding ordinary one. By using this form, we show that a noncommutative phase space of arbitrary dimension can be represented by the direct sum of two-dimensional noncommutative ones. In two-dimension, we obtain the transformation which relates a noncommutative phase space to commutative one. The transformation has the Lorentz transformation-like forms and can also describe the Bopp’s shift.

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

Digital Object Identifier: 10.7546/giq-22-2021-188-198

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

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