Dirac quantum walks with conserved angular momentum

Dirac quantum walks with conserved angular momentum

A quantum walk (QW) simulating the flat ( 1 + 2 ) D Dirac equation on a spatial polar grid is constructed. Because fermions are represented by spinors, which do not constitute a representation of the rotation group SO ( 3 ) , but rather of its double cover SU ( 2 ) , the QW can only be defined globa...

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Veröffentlicht in:Quantum Studies : Mathematics and Foundations 2021-11, Vol.8 (4), p.419-430
Hauptverfasser: Jay, Gareth, Arnault, Pablo, Debbasch, Fabrice
Format: Artikel
Sprache:eng
Schlagworte:
Angular momentum
Dirac equation
Electromagnetic fields
Fermions
History and Philosophical Foundations of Physics
Mathematical and Computational Physics
Mathematical Physics
Mathematics
Mathematics and Statistics
Physics
Quantum Physics
Regular Paper
Theoretical
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Zusammenfassung:A quantum walk (QW) simulating the flat ( 1 + 2 ) D Dirac equation on a spatial polar grid is constructed. Because fermions are represented by spinors, which do not constitute a representation of the rotation group SO ( 3 ) , but rather of its double cover SU ( 2 ) , the QW can only be defined globally on an extended spacetime where the polar angle extends from 0 to 4 π . The coupling of the QW with arbitrary electromagnetic fields is also presented. Finally, the cylindrical relativistic Landau levels of the Dirac equation are computed explicitly and simulated by the QW.
ISSN:2196-5609
2196-5617
DOI:10.1007/s40509-021-00253-x