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arXiv · 1911.08140

Non-existence theorems and solutions of the Wu-Yang monopole equation

Frederik Nørfjand·Nikolaj Thomas Zinner
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Abstract

We consider the dynamics of the classical $SU(2)$ Wu-Yang monopole problem and show a set of new directions for its analysis starting from a variational setting. This allows us to give a new interpretation of the monopole charge as a string in a centrifugal potential. The field equations are solved using both standard power series, as well as a new Pad\'e approach. Furthermore, we discuss non-existence, and give a proof that rule out even singular non-trivial smooth finite energy solutions. Due to its non-vanishing chromomagnetic fields, the monopole can be interpreted as a collection of magnetic dipoles. Along the same lines, a non-smooth glue-ball solution is discussed that may serve as a toy model of the proton or a radiation-dominated cosmological expansion. Finally, we discuss generalizations of the Wu-Yang monopole.

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Frederik Nørfjand, Nikolaj Thomas Zinner. 2019-11-19. Non-existence theorems and solutions of the Wu-Yang monopole equation. https://arxiv.org/abs/1911.08140

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