  The abelian Higgs model is studied on the lattice with charge conjugate
boundary conditions. A locally gauge invariant operator for the charged scalar
field is constructed and the charged scalar particle mass is calculated in the
Coulomb phase of the lattice model. Agreement is found with the mass calculated
in Coulomb gauge. The gauge invariant scalar field operator is used to
calculate the Higgs boson mass in the Higgs region and to show that the charged
particle disappears from the spectrum in the confined regime.
