Résumé
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.
| langue originale | Anglais |
|---|---|
| Numéro d'article | 061701 |
| journal | Physical Review D |
| Volume | 95 |
| Numéro de publication | 6 |
| Les DOIs | |
| état | Publié - 23 mars 2017 |
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Noncommutative geometry of Zitterbewegung. / Eckstein, Michał; Franco, Nicolas; Miller, Tomasz.
Dans: Physical Review D, Vol 95, Numéro 6, 061701, 23.03.2017.Résultats de recherche: Contribution à un journal/une revue › Article
TY - JOUR
T1 - Noncommutative geometry of Zitterbewegung
AU - Eckstein, Michał
AU - Franco, Nicolas
AU - Miller, Tomasz
PY - 2017/3/23
Y1 - 2017/3/23
N2 - 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.
AB - 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.
KW - noncommutative geometry
KW - Zitterbewegung
UR - http://www.scopus.com/inward/record.url?scp=85022344444&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.95.061701
DO - 10.1103/PhysRevD.95.061701
M3 - Article
VL - 95
JO - Physical Review D - Particles, Fields, Gravitation and Cosmology
JF - Physical Review D - Particles, Fields, Gravitation and Cosmology
SN - 1550-7998
IS - 6
M1 - 061701
ER -