Doubly special relativity from quantum cellular automata

Abstract

It is shown how a doubly special relativity model can emerge from a quantum cellular automaton description of the evolution of countably many interacting quantum systems. We consider a one-dimensional automaton that spawns the Dirac evolution in the relativistic limit of small wave vectors and masses (in Planck units). The assumption of invariance of dispersion relations for boosted observers leads to a non-linear representation of the Lorentz group on the -space, with an additional invariant given by the wave vector . The space-time reconstructed from the -space is intrinsically quantum, and exhibits the phenomenon of relative locality.