Noncommutative spacetimes versus noncommutative spaces of geodesics

Abstract

The aim of this contribution is twofold. First, we show that when two (or more) different quantum groups share the same noncommutative spacetime, such an 'ambiguity' can be resolved by considering together their corresponding noncommutative spaces of geodesics. In any case, the latter play a mathematical/physical role by themselves and, in some cases, they can be interpreted as deformed phase spaces. Second, we explicitly show that noncommutative spacetimes can be reproduced from 'extended' noncommutative spaces of geodesics which are those enlarged by the time translation generator. These general ideas are described in detail for the $\kappa$-Poincaré and $\kappa$-Galilei algebras.

11 pages. Based on the contribution presented at "The XII International Symposium on Quantum Theory and Symmetries" (QTS12), July 24-28, 2023, Czech Technical University in Prague, Czech Republic. To appear in Journal of Physics: Conference Series

References in corpus (2)

• Noncommutative spaces of worldlines
• Cayley-Klein Lie bialgebras: Noncommutative spaces, Drinfel'd doubles and kinematical applications