= Inverse-density Abelian Higgs model
{title2=$V=\tfrac12\int[B^2/h+|D\Phi|^2+h(1-h)^2/4],\quad h=|\Phi|^2$}
This planar <Abelian Higgs model> replaces the usual magnetic energy by $B^2/h$. Use $D_i=\partial_i-iA_i$ and $B=\partial_1A_2-\partial_2A_1$. The magnetic term is singular at a zero of the <Higgs field>, so the admissible class must have finite energy; formal field equations are first derived where $h>0$. Its positive-flux <Bogomolny equations> are $(D_1+iD_2)\Phi=0$ and $B=h(1-h)/2$. On those solutions $B/h=(1-h)/2$ extends regularly across zeros.
Back to article page
