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Noncommuting Momenta of Topological Solitons

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arxiv 1401.8139 v4 pith:ESSF3N3K submitted 2014-01-31 hep-th cond-mat.othercond-mat.quant-gashep-ph

Haruki Watanabe , Hitoshi Murayama This is my paper · ORCID
classification hep-thcond-mat.othercond-mat.quant-gashep-ph
keywords topologicalsolitonmomentumassociatedcohomologycommutationcommuteconstant
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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.

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  1. Anomalous Continuous Translations

    cond-mat.str-el 2024-12 accept novelty 5.0 of 10

    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.

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