The noncommutative geometry of Zitterbewegung

Abstract

Based on the 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 latter does not change in the presence of an external electromagnetic field and derive its explicit analogue when the mass parameter is promoted to a Higgs-like field. We discuss a table-top experiment in the domain of quantum simulation to test the predictions of the model and outline the consequences of our model for quantum gauge theories.

arXiv comment15 pages

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Cited by in corpus (9)

• The Lorentzian distance formula in noncommutative geometry
• Graviton corrections to the Newtonian potential using invariant observables
• Electron dynamics in noncommutative geometry with magnetic field and Zitterbewegung phenomenon
• Causality in noncommutative two-sheeted space-times
• Space and time dimensions of algebras with applications to Lorentzian noncommutative geometry and quantum electrodynamics
• Current Density of Majorana Bound States
• Quantum causality constraints on kappa-Minkowski space-time
• Quantum causality in $\kappa$-Minkowski and related constraints
• Physical models from noncommutative causality