Elongation of Moving Noncommutative Solitons

TL;DR

This paper investigates how noncommutative solitons behave when moving, revealing that their shapes can elongate transversely due to broken Lorentz symmetry, with examples from scalar fields and magnetic monopoles.

Contribution

It demonstrates that noncommutative solitons can elongate transversely when moving, showing this effect varies between different models and is not a universal phenomenon.

Findings

Moving noncommutative solitons exhibit transverse elongation.

Elongation factors differ between scalar and monopole cases.

Lorentz symmetry breaking influences soliton shape deformation.

Abstract

We discuss the characteristic properties of noncommutative solitons moving with constant velocity. As noncommutativity breaks the Lorentz symmetry, the shape of moving solitons is affected not just by the Lorentz contraction along the velocity direction, but also sometimes by additional `elongation' transverse to the velocity direction. We explore this in two examples: noncommutative solitons in a scalar field theory on two spatial dimension and `long stick' shaped noncommutative U(2) magnetic monopoles. However the elongation factors of these two cases are different, and so not universal.