Continuous translations are broken by an ABJ-like anomaly to a discrete non-Abelian symmetry in a broad class of non-relativistic continuum field theories.
Noncommuting Momenta of Topological Solitons
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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.
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Anomalous Continuous Translations
Continuous translations are broken by an ABJ-like anomaly to a discrete non-Abelian symmetry in a broad class of non-relativistic continuum field theories.