Existence of spinning solitons in gauge field theory

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 symmetric gauge fields the Noether charges corresponding to rigid spatial symmetries, as the angular momentum, can be expressed in terms of 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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