Classical aspects of the Abelian Higgs model on the light front

We investigate canonical structure of the Abelian Higgs model within the fr amework of DLCQ. Careful boundary analysis of differential equations, such as the Euler-Lagrange equations, leads us to a novel situation where the ca nonical structure changes in a drastic manner depending on whether the (lig ht-front) spatial Wilson line is periodic or not. In the former case, the g auge-field ZM takes discrete values and we obtain so-called "Zero-Mode Cons traints" (ZMCs), whose semiclassical solutions give a nonzero vev to the sc alar fields. Contrary, in the latter case, we have no ZMC and the scalar ZM s remain dynamical as well as the gauge-field ZM. In order to give classica lly the nonzero vev to the scalar field, we work in a background field whic h minimizes the light-front energy. (C) 1998 Elsevier Science B.V. All righ ts reserved.