Foundations of Physics

, Volume 45, Issue 10, pp 1203–1221 | Cite as

Weyl, Dirac and Maxwell Quantum Cellular Automata

Analitical Solutions and Phenomenological Predictions of the Quantum Cellular Automata Theory of Free Fields
  • Alessandro Bisio
  • Giacomo Mauro D’Ariano
  • Paolo PerinottiEmail author
  • Alessandro Tosini


Recent advances on quantum foundations achieved the derivation of free quantum field theory from general principles, without referring to mechanical notions and relativistic invariance. From the aforementioned principles a quantum cellular automata (QCA) theory follows, whose relativistic limit of small wave-vector provides the free dynamics of quantum field theory. The QCA theory can be regarded as an extended quantum field theory that describes in a unified way all scales ranging from an hypothetical discrete Planck scale up to the usual Fermi scale. The present paper reviews the automaton theory for the Weyl field, and the composite automata for Dirac and Maxwell fields. We then give a simple analysis of the dynamics in the momentum space in terms of a dispersive differential equation for narrowband wave-packets. We then review the phenomenology of the free-field automaton and consider possible visible effects arising from the discreteness of the framework. We conclude introducing the consequences of the automaton dispersion relation, leading to a deformed Lorentz covariance and to possible effects on the thermodynamics of ideal gases.


Quantum field theory Quantum cellular automata Quantum walks 



This work has been supported in part by the Templeton Foundation under the Project ID# 43796 A Quantum-Digital Universe.


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.QUIT GroupDipartimento di Fisica and INFN sezione di PaviaPaviaItaly

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