# The noncommutative geometry of Zitterbewegung

October 31, 2016

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.

Keywords:

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