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EnglishWithout 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 Schroedinger equation describing the evolution of narrowband states at all scales.
Derivation of the Dirac equation from principles of information processing / Giacomo Mauro D'Ariano;Paolo Perinotti. - In: PHYSICAL REVIEW A. - ISSN 1050-2947. - STAMPA. - 90(2014), pp. 062106-01-062106-18.
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| Titolo: | Derivation of the Dirac equation from principles of information processing |
| Autori: | |
| Data di pubblicazione: | 2014 |
| Rivista: | |
| Citazione: | Derivation of the Dirac equation from principles of information processing / Giacomo Mauro D'Ariano;Paolo Perinotti. - In: PHYSICAL REVIEW A. - ISSN 1050-2947. - STAMPA. - 90(2014), pp. 062106-01-062106-18. |
| Abstract: | 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 Schroedinger equation describing the evolution of narrowband states at all scales. |
| Handle: | http://hdl.handle.net/11571/981531 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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