Generalized Relativistic Kinematics

Abstract

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.

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Cited by in corpus (2)

• Universal constants and natural systems of units in a spacetime of arbitrary dimension
• Noether Charge, Thermodynamics and Phase Transition of a Black Hole in the Schwarzschild-Anti-de Sitter-Beltrami spacetime