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Pointlike Hopf defects in Abelian projections

Falk Bruckmann
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Abstract

We present a new kind of defect in Abelian Projections, stemming from pointlike zeros of second order. The corresponding topological quantity is the Hopf invariant pi_3(S^2) (rather than the winding number pi_2(S^2) for magnetic monopoles). We give a visualisation of this quantity and discuss the simplest non-trivial example, the Hopf map. Such defects occur in the Laplacian Abelian gauge in a non-trivial instanton sector. For general Abelian projections we show how an ensemble of Hopf defects accounts for the instanton number.

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Falk Bruckmann. 2000-12-01. Pointlike Hopf defects in Abelian projections. https://doi.org/10.1142/9789812811455_0012

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