One-Dimensional Fermions as Two-Dimensional Droplets Via Chern-Simons Theory
Abstract
Based on the observation that a particle motion in one dimension maps to a two-dimensional motion of a charged particle in a uniform magnetic field, constrained in the lowest Landau level, we formulate a system of one-dimen- sional nonrelativistic fermions by using a Chern-Simons field theory in 2+1 dimensions. Using a hydrodynamical formulation we obtain a two-dimensional droplet picture of one-dimensional fermions. The dynamics involved is that of the boundary between a uniform density of particles and vortices. We use the sharp boundary approximation. In the case of well separated boundaries we derive the one-dimensional collective field Hamiltonian. Symmetries of the theory are also discussed as properties of curves in two dimensions.
Cite
@article{arxiv.hep-th/9202012,
title = {One-Dimensional Fermions as Two-Dimensional Droplets Via Chern-Simons Theory},
author = {Satoshi Iso and Dimitra Karabali and B. Sakita},
journal= {arXiv preprint arXiv:hep-th/9202012},
year = {2009}
}
Comments
19 pages (2 figures are not included)