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A relativistic wave equation for the Skyrmion. (English) Zbl 1152.81843

Summary: We propose a relativistically invariant wave equation for the Skyrme soliton. It is a differential equation on the space \(\mathbb R^{1,3}\times S^{3}\) which is invariant under the Lorentz group and isospin. The internal variable valued in \(SU(2)\equiv S^{3}\) describes the orientation of the soliton. The mass of a particle of spin and isospin both equal to \(j= \frac 1 2 , \frac 3 2 , \dots \) is predicted to be \(M = m\sqrt{\frac{1+K_2j(j+1)}{1+K_1j(j+1)}}\) which agrees with the known spectrum for low angular momentum. The iso-scalar magnetic moment is predicted to be \(\frac {-K_1}{43}\Sigma \), where \(\Sigma \) is the spin.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
70G40 Topological and differential topological methods for problems in mechanics
81V35 Nuclear physics

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