Symmetry breaking in Landau gauge a comment to a paper by T. Kennedy and C. King

Abstract

For the non-compact abelian lattice Higgs model in Landau gauge Kennedy and King (Princeton preprint, 1985) showed that the two point function$\langle \phi (x)\bar \phi (y)\rangle$ does not decay in the Higgs phase. We generalize their methods to show that for the same range of parameters there are states parametrized by an angle θ∈[0, 2π) such that$\langle \phi (x)\rangle _{Landau}^\theta = e^{i\theta } \langle \phi (x)\rangle _{Landau}^{\theta = 0}$ and$\langle \phi (x)\rangle _{Landau}^{\theta = 0} > 0$.