Spontaneous symmetry breaking and Higgs mechanism in a light front formulation

A semiclassical picture of spontaneous symmetry breaking in light front field theory is formulated. It is based on a finite-volume quantization of self-interacting scalar fields obeying antiperiodic boundary conditions. This avoids a necessity to solve the zero mode constraint and simultaneously enables one to define unitary operators which shift scalar field by a constant. These operators transform the light-front Fock vacuum to coherent states with lower energy than the original vacuum. The new vacuum states are nonivariant under the discrete or continuous symmetry of the Hamiltonian. Spontaneous symmetry breaking is described in this way in the two-dimensional λϕ4 theory and in the four-dimensional abelian Higgs model. In the latter case, the physically relevant Hamiltonian describes a massive vector field while the massless scalar field decouples. This mechanism, understood here quantum mechanically in the form analogous to the spacelike quantization, is derived without gauge fixing as well as in the unitary gauge.