Volume 109, Number 5, March 2015
|Number of page(s)||5|
|Published online||12 March 2015|
Doubly special relativity from quantum cellular automata
1 Département IRO, Université de Montréal - Montréal H3C 3J7, Canada
2 QUIT group, Dipartimento di Fisica - via Bassi 6, 27100 Pavia, Italy
3 INFN Sezione di Pavia - via Bassi, 6, 27100 Pavia, Italy
Received: 15 October 2014
Accepted: 16 February 2015
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.
PACS: 03.65.Ta – Foundations of quantum mechanics; measurement theory / 03.67.Ac – Quantum algorithms, protocols, and simulations
© EPLA, 2015
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