Foundations of Physics

, Volume 45, Issue 10, pp 1137–1152 | Cite as

Free Quantum Field Theory from Quantum Cellular Automata

Derivation of Weyl, Dirac and Maxwell Quantum Cellular Automata
  • Alessandro Bisio
  • Giacomo Mauro D’ArianoEmail author
  • Paolo Perinotti
  • Alessandro Tosini


After leading to a new axiomatic derivation of quantum theory (see D’Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).


Informational principles Quantum field theory Quantum cellular automata Planck scale 



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


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Alessandro Bisio
    • 1
  • Giacomo Mauro D’Ariano
    • 1
    Email author
  • Paolo Perinotti
    • 1
  • Alessandro Tosini
    • 1
  1. 1.QUIT Group, Dipartimento di FisicaUniversita’ di Pavia and INFN sezione di PaviaPaviaItaly

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