MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

The Topology of the Electroweak Interaction

Jürgen Tolksdorf


In this paper we show that the Higgs boson of the (minimal) Standard Model has at most three gauge inequivalent ground states. One of these states is related to ordinary electromagnetism and the other two to electromagnetism within magnetically charged vacua. If space-time is assumed to be rotationally symmetric then the charged electroweak vacua may be identified with Dirac monopoles of magnetic charge ${\rm g}=\pm1/2$. This offers a physical interpretation of magnetic monopoles and Dirac's quantization condition of electric charge in terms of the electroweak interaction. Moreover, in the case of the (minimal) Standard Model the three possible gauge inequivalent ground states of the Higgs boson are shown to fully determine the topological structure of the gauge bundle which underlies the electroweak interaction.

MSC Codes:
53C80, 55R10, 70S05, 70S15, 81V15
02.40.MA, 11.15.Ex, 12.15.-y
bundle topology, magnetic monopoles, electroweak interaction, charge quantization

Related publications

2005 Repository Open Access
Jürgen Tolksdorf

The topology of the electroweak interaction

In: Journal of mathematical physics, 46 (2005) 4, p. 042304