Noncommuting Momenta of Topological Solitons

Abstract

We show that momentum operators of a topological soliton may not commute among themselves when the soliton is associated with the second cohomology $H^2$ of the target space. The commutation relation is proportional to the winding number, taking a constant value within each topological sector. The noncommutativity makes it impossible to specify the momentum of a topological soliton, and induces a Magnus force.

Comments: 5 +1 pages, including Supplemental Material; v4: new references added, published version