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.

References in corpus (5)

• Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes
• Snyder's Model -- de Sitter Special Relativity Duality and de Sitter Gravity
• Snyder's Quantized Space-time and De Sitter Special Relativity
• The Principle of Relativity and Special Relativity Triple
• On de Sitter Invariant Special Relativity and Cosmological Constant as Origin of Inertia

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