Noncommutative geometry of Zitterbewegung

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 wel...

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Bibliographic Details
Published in:Physical review. D 2017-03, Vol.95 (6), Article 061701
Main Authors: Eckstein, Michał, Franco, Nicolas, Miller, Tomasz
Format: Article
Language:English
Subjects:
Computer simulation
Electromagnetic fields
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Summary: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.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.95.061701