Journal of Geometry and Symmetry in Physics

Some Strange Features of the Galilei Group

Barbara Gołubowska, Vasyl Kovalchuk, Agnieszka Martens, Ewa Eliza Rozko, and Jan J. Sławianowski

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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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J. Geom. Symmetry Phys., Volume 26 (2012), 33-59.

First available in Project Euclid: 25 May 2017

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

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