"Peireles Substitution" and Chern-Simons Quantum Mechanics
Gerald Dunne, Roman Jackiw
TL;DR
This paper provides an elementary derivation of the Peierles substitution, clarifying its role in projecting quantum dynamics onto the lowest Landau level in strong magnetic fields.
Contribution
It offers a new, simplified derivation and explanation of the Peierles substitution and the associated Hamiltonian ordering in quantum mechanics under magnetic fields.
Findings
Clarifies the derivation of Peierles substitution
Explains the projection of wavefunctions onto the lowest Landau level
Details the ordering prescription for the projected Hamiltonian
Abstract
An elementary derivation is given for the ``Peierles substitution'' used in projecting dynamics in a strong magnetic field onto the lowest Landau level. The projection of wavefunctions and the ordering prescription for the projected Hamiltonian is explained.
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