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Existence of spinning solitons in gauge field theory

Mikhail S. Volkov·Erik Woehnert
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Abstract

We study the existence of classical soliton solutions with intrinsic angular momentum in Yang-Mills-Higgs theory with a compact gauge group $\mathcal{G}$ in (3+1)-dimensional Minkowski space. We show that for \textit{symmetric} gauge fields the Noether charges corresponding to \textit{rigid} spatial symmetries, as the angular momentum, can be expressed in terms of \textit{surface} integrals. Using this result, we demonstrate in the case of $\mathcal{G}=SU(2)$ the nonexistence of stationary and axially symmetric spinning excitations for all known topological solitons in the one-soliton sector, that is, for 't Hooft--Polyakov monopoles, Julia-Zee dyons, sphalerons, and also vortices.

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Mikhail S. Volkov, Erik Woehnert. 2003-05-06. Existence of spinning solitons in gauge field theory. https://doi.org/10.1103/physrevd.67.105006

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