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arXiv · 1406.1021

Path-integral solution of the one-dimensional Dirac quantum cellular automaton

Giacomo Mauro D'Ariano·Nicola Mosco·Paolo Perinotti·Alessandro Tosini
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Abstract

Quantum cellular automata have been recently considered as a fundamental approach to quantum field theory, resorting to a precise automaton, linear in the field, for the Dirac equation in one dimension. In such linear case a quantum automaton is isomorphic to a quantum walk, and a convenient formulation can be given in terms of transition matrices, leading to a new kind of discrete path integral that we solve analytically in terms of Jacobi polynomials versus the arbitrary mass parameter.

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Giacomo Mauro D'Ariano, Nicola Mosco, Paolo Perinotti, Alessandro Tosini. 2014-06-04. Path-integral solution of the one-dimensional Dirac quantum cellular automaton. https://doi.org/10.1016/j.physleta.2014.09.020

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