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.

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

References in corpus (7)

• Spontaneous Skyrmion Ground States in Magnetic Metals
• Long wavelength helimagnetic order and skyrmion lattice phase in Cu2OSeO3
• Theory of the helical spin crystal: a candidate for the partially ordered state of MnSi
• Formation and rotation of skyrmion crystal in the chiral-lattice insulator Cu2OSeO3
• Counting rule for Nambu-Goldstone modes in nonrelativistic systems
• Theory of helical spin crystals: phases, textures and properties
• Crystalline phases in chiral ferromagnets: Destabilization of helical order

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