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

By Fabrice Debbasch

Abstract

International audienceA 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

Topics: Lorentz invariance, Energy-momentum conservation, Action principle, Quantum automaton, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], [PHYS]Physics [physics], [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph]
Publisher: 'Elsevier BV'
Year: 2019
DOI identifier: 10.1016/j.aop.2019.03.005
OAI identifier: oai:HAL:hal-01818133v1
Provided by: HAL-INSU
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