Instability of electroweak homogeneous vacua in strong magnetic fields
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866910347751849984 |
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| author | Gardner, Adam Sigal, Israel Michael |
| author_facet | Gardner, Adam Sigal, Israel Michael |
| contents | 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 plan 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_00769 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Instability of electroweak homogeneous vacua in strong magnetic fields Gardner, Adam Sigal, Israel Michael Mathematical Physics 81T13 (primary), 35Q40, 70S15 (secondary) 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 plan 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. |
| title | Instability of electroweak homogeneous vacua in strong magnetic fields |
| topic | Mathematical Physics 81T13 (primary), 35Q40, 70S15 (secondary) |
| url | https://arxiv.org/abs/2211.00769 |