Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields

TL;DR

This paper investigates time-dependent soliton solutions in noncommutative Chern-Simons theory coupled to scalar fields, revealing new stationary solutions and analyzing their moduli space structure.

Contribution

It introduces novel time-dependent soliton solutions in noncommutative Chern-Simons theory with scalar fields and explores their moduli space properties.

Findings

Found a tower of stationary solutions with same charge but increasing energy

Identified a nontrivial symplectic form indicating non-flat moduli space

Derived the metric on the two-soliton moduli space in the relativistic case

Abstract

We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case, we find a tower of new stationary time-dependent solutions, all with the same charge density, but with increasing energies. The dynamics of these solitons cannot be studied using traditional moduli space techniques, but we do find a nontrivial symplectic form on the phase space indicating that the moduli space is not flat. In the relativistic case we find the metric on the two soliton moduli space.