Non-commutative Soliton Scattering

TL;DR

This paper investigates the properties and scattering behavior of solitons in a three-dimensional non-commutative scalar field theory, revealing a Kahler metric on moduli space and right-angle scattering at small impact parameters.

Contribution

It demonstrates that the moduli space of solitons is Kahler and analyzes their scattering, showing right-angle scattering due to a conical singularity.

Findings

Moduli space metric is Kahler.

Soliton scattering is generally at right angles.

Conical singularity explains scattering behavior.

Abstract

We study solitons in three dimensional non-commutative scalar field theory at infinite non-commutativity parameter. We find the metric on the relative moduli space of all solitons of the form |n><n| and show that it is Kahler. We then find the geodesics of this metric and study the scattering of these solitons. In particular we find that the scattering is generally right angle for small values of the impact parameter. We can understand this behaviour in terms of a conical singularity at the origin of moduli space.