Instability of electroweak homogeneous vacua in strong magnetic fields

arXiv2211.00769MaRDI QIDQ6508130

I. M. Sigal, Adam Gardner

Abstract: 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.

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) PDEs in connection with quantum mechanics (35Q40) Yang-Mills and other gauge theories in mechanics of particles and systems (70S15)

This page was built for publication: Instability of electroweak homogeneous vacua in strong magnetic fields

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6508130)