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Article Dans Une Revue Annals Phys. Année : 2019

Action Principles for Quantum Automata and Lorentz Invariance of Discrete Time Quantum Walks

Résumé

A discrete action principle for general quantum automata is proposed. This action principle is particularized to Discrete Time Quantum Walks (DTQWs) and then extended into an energy and momentum preserving, manifestly covariant formulation. Space–time coordinates are introduced as new variables of the action and their equations of motion enforce energy and momentum conservation. This guarantees that the proposed action can be used to build future, DTQW-based self-consistent models of spinors interacting with gauge fields. A discrete stress–energy tensor for the DTQW is also obtained. The manifest covariance of the formulation highlights the special role played by the grid reference frame in the DTQW dynamics. The main discussion is complemented by three appendices.
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Dates et versions

hal-01818133 , version 1 (22-10-2021)

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Fabrice Debbasch. Action Principles for Quantum Automata and Lorentz Invariance of Discrete Time Quantum Walks. Annals Phys., 2019, 405, pp.340-364. ⟨10.1016/j.aop.2019.03.005⟩. ⟨hal-01818133⟩
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