Spontaneous symmetry breakdown in the abelian Higgs model

For the abelian Higgs model we introduce a new gauge invariant observable which in Landau gauge is. In three or more dimensions this observable is used to show that the global gauge symmetry is spontaneously broken in the lattice theory for a suitable range of parameters. This observable also provides a gauge invariant order parameter for the phase transition in this model.Research supported by U.S. National Science Foundation grant PHY8116101-A03Research supported by U.S. National Science Foundation grant PHY8117463