Analitical Solutions and Phenomenological Predictions of the Quantum Cellular Automata Theory of Free Fields
Alessandro Bisio, Giacomo Mauro D’Ariano, Paolo Perinotti, Alessandro Tosini · 2015
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)theoryfollows,whoserelativisticlimitofsmallwave-vectorprovides 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 Weylfield, 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 visibleeffectsarisingfromthediscretenessoftheframework.Weconcludeintroducing the consequences of the automaton dispersion relation, leading to a deformed Lorentz covariance and to possible effects on the thermodynamics of ideal gases.