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. 2019 Dec 30;377(2161):20180327.
doi: 10.1098/rsta.2018.0327. Epub 2019 Nov 11.

The inevitability of sphalerons in field theory

N S Manton  1
Affiliations

The inevitability of sphalerons in field theory

N S Manton. Philos Trans A Math Phys Eng Sci. .

Abstract

The topological structure of field theory often makes inevitable the existence of stable and unstable localized solutions of the field equations. These are minima and saddle points of the energy. Saddle point solutions occurring this way are known as sphalerons, and the most interesting one is in the electroweak theory of coupled W, Z and Higgs bosons. The topological ideas underpinning sphalerons are reviewed here. This article is part of a discussion meeting issue 'Topological avatars of new physics'.

Keywords: electroweak theory; saddle point; sphaleron; topology.

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Conflict of interest statement

I declare I have no competing interests.

Figures

Figure 1.
Figure 1.
B = 1 Skyrmion (two different orientations). (Online version in colour.)
Figure 2.
Figure 2.
B = 4 Skyrmion. (Online version in colour.)
Figure 3.
Figure 3.
B = 8 Skyrmion. (Online version in colour.)
Figure 4.
Figure 4.
B = 12 Skyrmion with D3h symmetry. (Online version in colour.)
Figure 5.
Figure 5.
B = 12 Skyrmion with D4h symmetry. (Online version in colour.)
See this image and copyright information in PMC

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