International Association for
Relativistic Dynamics

IARD 2020

The 12th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields

Coherent states for generalized uncertainty relations and their cosmological implications

Petr Jizba

Czech Technical University in Prague


In my talk I will evaluate the exact expression for the coherent states associated to a generalized uncertainty principle (GUP) known from double-special relativity. In particular, I will show that the probability distribution related to such states is actually a Tsallis distribution, whose non-extensivity parameter q is linearly related to the Magueijo and Smolin deformation parameter . In the limit when , I will recover the Maxwell-Jüttner distribution for relativistic particles.

I further will show the connection of the analyzed GUP with Tsallis and Rényi entropic uncertainty relations that are currently important in quantum metrology. In the final part of my talk I will discuss various cosmological bounds on the Tsallis parameter , which in turn provide a severe restriction of the cosmologically feasible GUP.

Work in preparation.