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VOL. 13 | 2012 Some Strange Features of the Galilei Group
Barbara Gołubowska, Vasyl Kovalchuk, Agnieszka Martens, Ewa E. Rożko, Jan J. Sławianowski

Editor(s) Ivaïlo M. Mladenov, Andrei Ludu, Akira Yoshioka


Discussed are certain strange properties of the Galilei group, connected first of all with the property of mechanical energy-momentum covector to be an affine object, rather than the linear one. Its affine transformation rule is interesting in itself and dependent on the particle mass. On the quantum level this means obviously that we deal with the projective unitary representation of the group rather than with the usual representation. The status of mass is completely different than in relativistic theory, where it is a continuous eigenvalue of the Casimir invariant. In Galilei framework it is a parameter characterizing the factor of the projective representation, in the sense of V. Bargmann. This “pathology” from the relativistic point of view is nevertheless very interesting and it underlies the Weyl-Wigner-Moyal-Ville approach to quantum mechanics.


Published: 1 January 2012
First available in Project Euclid: 13 July 2015

zbMATH: 1382.81109
MathSciNet: MR3087969

Digital Object Identifier: 10.7546/giq-13-2012-150-175

Rights: Copyright © 2012 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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