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.

15 pages

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Cited by in corpus (6)

• Graviton corrections to the Newtonian potential using invariant observables
• Causality in noncommutative two-sheeted space-times
• Electron dynamics in noncommutative geometry with magnetic field and Zitterbewegung phenomenon
• Current Density of Majorana Bound States
• Quantum causality constraints on kappa-Minkowski space-time
• Quantum causality in $\kappa$-Minkowski and related constraints