Chern-Simons Soliton Dynamics in Modular Parameter Space

TL;DR

This paper investigates the dynamics of non-relativistic Chern-Simons solitons, revealing the importance of a phase related to the Galileo group and analytically deriving the effective interaction between two solitons.

Contribution

It introduces the necessity of a Galileo-related phase for correct dynamics and provides an analytical form of the two-soliton interaction Lagrangian.

Findings

A phase related to the Galileo group is essential for accurate soliton dynamics.

Interactions are mediated by an effective Chern-Simons gauge field.

Analytical expression for the two-soliton interaction was derived.

Abstract

We study dynamics of non-relativistic Chern-Simons solitons, both in the absence and in the presence of external fields. We find that a phase, related to the $1$-cocyle of the Galileo group, must be included to give the correct dynamical behavior. We show that interactions among Chern-Simons solitons are mediated by an effective Chern-Simons gauge field induced by the solitons. In the two soliton case, we evaluate analytically the effective interaction Lagrangian, which previously was found numerically.