  We investigate canonical structure of the Abelian Higgs model within the
framework of DLCQ. Careful boundary analysis of differential equations, such as
the Euler-Lagrange equations, leads us to a novel situation where the canonical
structure changes in a drastic manner depending on whether the (light-front)
spatial Wilson line is periodic or not. In the former case, the gauge-field ZM
takes discrete values and we obtain the so-called ``Zero-Mode Constraints''
(ZMCs), whose semiclassical solutions give a nonzero vev to the scalar fields.
Contrary, in the latter case, we have no ZMC and the scalar ZMs remain
dynamical as well as the gauge-field ZM. In order to give classically nonzero
vev to the scalar field, we work in a background field which minimizes the
light-front energy.
