Open Access
2012 Some Strange Features of the Galilei Group
Barbara Gołubowska, Vasyl Kovalchuk, Agnieszka Martens, Ewa Eliza Rozko, Jan J. Sławianowski
J. Geom. Symmetry Phys. 26: 33-59 (2012). DOI: 10.7546/jgsp-26-2012-33-59


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.


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Barbara Gołubowska. Vasyl Kovalchuk. Agnieszka Martens. Ewa Eliza Rozko. Jan J. Sławianowski. "Some Strange Features of the Galilei Group." J. Geom. Symmetry Phys. 26 33 - 59, 2012.


Published: 2012
First available in Project Euclid: 25 May 2017

zbMATH: 1262.81065
MathSciNet: MR2986251
Digital Object Identifier: 10.7546/jgsp-26-2012-33-59

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

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