2022/11/01 by Adam Gardner, Israel Michael Sigal, Gardner, Adam +1
Physics and Astronomy · #35Q40 #70S15 (secondary) #81T13 (primary) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Physics of Superconductivity and Magnetism #Quantum, superfluid, helium dynamics
paper · pdf · doi:10.48550/arxiv.2211.00769
openalex publication_date 2022/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.