Thursday, December 13, 2012

1212.2839 (Alessandro Bisio et al.)

Quantum Field as a Quantum Cellular Automaton I: the Dirac free
evolution in one dimension
   [PDF]

Alessandro Bisio, Giacomo Mauro D'Ariano, Alessandro Tosini
It is shown how a quantum cellular automaton can describe very precisely the Dirac evolution, without requiring Lorentz covariance. The automaton is derived with the only assumptions of minimal dimension and parity and time-reversal invariance. The automaton extends the Dirac field theory to the Planck and ultrarelativistic scales. The Dirac equation is recovered in the usual particle physics scale of inertial mass and momenta. In this first paper the simplest case of one space dimension is analyzed. We provide a technique to derive an analytical approximation of the evolution of the automaton in terms of a momentum-dependent Schroedinger equation. Such approximation works very well in all regimes, including ultrarelativistic and Planckian, for the typical smooth quantum states of field theory with limited bandwidth in momentum. Finally we discuss some thought experiments for falsifying the existence of the automaton at the Planck scale.
View original: http://arxiv.org/abs/1212.2839

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