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.