Generalized relativistic kinematics
Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 2, pp. 323-336
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We propose a method for deforming an extended Galilei algebra that leads to a nonstandard realization of the Poincaré group with the Fock–Lorentz linear fractional transformations. The invariant parameter in these transformations has the dimension of length. Combining this deformation with the standard one (with an invariant velocity $c$) leads to the algebra of the symmetry group of the anti-de Sitter space in Beltrami coordinates. In this case, the action for free point particles contains the dimensional constants $R$ and $c$. The limit transitions lead to the ordinary ($R\to\infty$) or alternative ($c\to\infty$) but nevertheless relativistic kinematics.
Keywords:
principle of relativity, relativistic kinematics, Galilei algebra, Poincaré group, anti-de Sitter space.
@article{TMF_2011_169_2_a12,
author = {S. N. Manida},
title = {Generalized relativistic kinematics},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {323--336},
publisher = {mathdoc},
volume = {169},
number = {2},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2011_169_2_a12/}
}
S. N. Manida. Generalized relativistic kinematics. Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 2, pp. 323-336. http://geodesic.mathdoc.fr/item/TMF_2011_169_2_a12/