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Instability of Electroweak Homogeneous Vacua in Strong Magnetic Fields
We consider the classical vacua of the Weinberg–Salam (WS) model of electroweak forces. These are no-particle, static solutions to the WS equations minimizing the WS energy locally. We study the WS vacuum solutions exhibiting a non-vanishing average magnetic field of strength b and prove that (i) th...
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Published in: | Annales Henri Poincaré 2024, Vol.25 (12), p.5277-5337 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites |
Online Access: | Get full text |
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Summary: | We consider the classical vacua of the Weinberg–Salam (WS) model of electroweak forces. These are no-particle, static solutions to the WS equations minimizing the WS energy locally. We study the WS vacuum solutions exhibiting a non-vanishing average magnetic field of strength
b
and prove that (i) there is a magnetic field threshold
b
∗
such that for
b
<
b
∗
, the vacua are translationally invariant (and the magnetic field is constant), while, for
b
>
b
∗
, they are not, (ii) for
b
>
b
∗
, there are non-translationally invariant solutions with lower energy per unit volume and with the discrete translational symmetry of a 2D lattice in the plane transversal to
b
, and (iii) the lattice minimizing the energy per unit volume approaches the hexagonal one as the magnetic field strength approaches the threshold
b
∗
. In the absence of particles, the Weinberg–Salam model reduces to the Yang–Mills–Higgs (YMH) equations for the gauge group
U
(2). Thus, our results can be rephrased as the corresponding statements about the
U
(2)-YMH equations. |
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ISSN: | 1424-0637 1424-0661 |
DOI: | 10.1007/s00023-024-01430-5 |