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arXiv · hep-th/0105141

Classical Gauge Vacua as Knots

Pierre van Baal·Andreas Wipf
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Abstract

The four dimensional O(3) non-linear sigma model introduced by Faddeev and Niemi, with a Skyrme-like higher order term to stabilise static knot solutions classified by the Hopf invariant, can be rewritten in terms of the complex two-component CP1 variables. A further rewriting of these variables in terms of SU(2) curvature free gauge fields is performed. This leads us to interpret SU(2) pure gauge vacuum configurations, in a particular maximal abelian gauge, in terms of knots with the Hopf invariant equal to the winding number of the gauge configuration.

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Pierre van Baal, Andreas Wipf. 2001-05-15. Classical Gauge Vacua as Knots. https://doi.org/10.1016/s0370-2693(01)00856-5

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