A Nonrelativistic Chiral Soliton in One Dimension
High Energy Physics - Theory
2015-06-26 v1 Condensed Matter
dg-ga
Differential Geometry
Exactly Solvable and Integrable Systems
Quantum Physics
solv-int
Abstract
I analyze the one-dimensional, cubic Schr\"odinger equation, with nonlinearity constructed from the current density, rather than, as is usual, from the charge density. A soliton solution is found, where the soliton moves only in one direction. Relation to higher-dimensional Chern--Simons theory is indicated. The theory is quantized and results for the two-body quantum problem agree at weak coupling with those coming from a semiclassical quantization of the soliton.
Keywords
Cite
@article{arxiv.hep-th/9611185,
title = {A Nonrelativistic Chiral Soliton in One Dimension},
author = {R. Jackiw},
journal= {arXiv preprint arXiv:hep-th/9611185},
year = {2015}
}
Comments
11 pages, Latex2e