2013/06/30 by Giacomo Mauro D’Ariano, G. M. D'Ariano, Paolo Perinotti +1
Physics and Astronomy · #Causal fermion system #Classical mechanics #Dirac equation #Dirac fermion #Dirac sea #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Schrödinger equation #Theory of relativity #Two-body Dirac equations #hep-th #quant-ph
paper · pdf · doi:10.1103/physreva.90.062106
published as Phys. Rev. A 90, 062106 (2014) · 20 pages, 9 figures, revtex4, revised version
openalex publication_date 2014/12/02 · arxiv created 2014/12/28 · arxiv updated 2014/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Without using the relativity principle, we show how the Dirac equation in three space dimensions emerges from the large-scale dynamics of the minimal nontrivial quantum cellular automaton satisfying unitarity, locality, homogeneity, and discrete isotropy. The Dirac equation is recovered for small wave vector and inertial mass, whereas Lorentz covariance is distorted in the ultrarelativistic limit. The automaton can thus be regarded as a theory unifying scales from Planck to Fermi. A simple asymptotic approach leads to a dispersive Schr"odinger equation describing the evolution of narrowband states at all scales.