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Noncommutative geometry of Zitterbewegung

Michał Eckstein, Nicolas Franco, and Tomasz Miller
Phys. Rev. D 95, 061701(R) – Published 23 March 2017

Abstract

Drawing from the advanced mathematics of noncommutative geometry, we model a “classical” Dirac fermion propagating in a curved spacetime. We demonstrate that the inherent causal structure of the model encodes the possibility of Zitterbewegung—the “trembling motion” of the fermion. We recover the well-known frequency of Zitterbewegung as the highest possible speed of change in the fermion’s “internal space.” Furthermore, we show that the bound does not change in the presence of an external electromagnetic field and derive its explicit analogue when the mass parameter is promoted to a Yukawa field. We explain the universal character of the model and discuss a table-top experiment in the domain of quantum simulation to test its predictions.

  • Received 24 December 2016

DOI:https://doi.org/10.1103/PhysRevD.95.061701

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Particles & FieldsGeneral Physics

Authors & Affiliations

Michał Eckstein1,2,*, Nicolas Franco3,2,†, and Tomasz Miller4,2,‡

  • 1Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. prof. Stanisława Łojasiewicza 11, 30-348 Kraków, Poland
  • 2Copernicus Center for Interdisciplinary Studies, ul. Szczepańska 1/5, 31-011 Kraków, Poland
  • 3Namur Center for Complex Systems (naXys) & Department of Mathematics, University of Namur, Rue de Bruxelles 61, 5000 Namur, Belgium
  • 4Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland

  • *michal.eckstein@uj.edu.pl
  • nicolas.franco@math.unamur.be
  • t.miller@mini.pw.edu.pl

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Issue

Vol. 95, Iss. 6 — 15 March 2017

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