Symmetries of the pre-Klein-Gordon bundle: a Lagrangian analysis of quantum relativistic symmetry
- 1 October 1985
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 18 (14) , 2639-2646
- https://doi.org/10.1088/0305-4470/18/14/015
Abstract
The authors discuss the Lagrangian formulation of a group theoretical quantisation procedure where the rest mass of a scalar relativistic particle is introduced by putting a restriction (the mass shell condition) on the manifold of a group, G15, defining a larger symmetry. This group is obtained through one of the possible contractions of the conformal group and, because of its non-trivial cohomology, G15 allows for a central quantum U(1)-extension. Besides illustrating the appearance of the mass term in the relativistic Lagrangian as a consequence of reducing the symmetry, the Klein-Gordon 'probability' current is obtained as the one associated to a relativistic central symmetry.Keywords
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