Proceedings of the International Conference on Geometry, Integrability and Quantization

Some Strange Features of the Galilei Group

Barbara Gołubowska, Vasyl Kovalchuk, Agnieszka Martens, Ewa E. Rożko, and Jan J. Sławianowski

Abstract

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.

Article information

Source
Proceedings of the Thirteenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Andrei Ludu and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2012), 150-175

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436815523

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

Mathematical Reviews number (MathSciNet)
MR3087969

Zentralblatt MATH identifier
1382.81109

Citation

Gołubowska, Barbara; Kovalchuk, Vasyl; Martens, Agnieszka; Rożko, Ewa E.; Sławianowski, Jan J. Some Strange Features of the Galilei Group. Proceedings of the Thirteenth International Conference on Geometry, Integrability and Quantization, 150--175, Avangard Prima, Sofia, Bulgaria, 2012. doi:10.7546/giq-13-2012-150-175. https://projecteuclid.org/euclid.pgiq/1436815523


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