Scattering from a Domain Wall in a Spontaneously Broken Gauge Theory

We study the interaction of particles with a domain wall at a symmetry-breaking phase transition by perturbing about the domain wall solution. We find the particulate excitations appropriate near the domain wall and relate them to the particles present far from the wall in the uniform broken and unbroken phases. For a quartic Higgs potential we find analytic solutions to the equations of motion and derive reflection and transmission coefficients. We discover several bound states for particles near the wall. Finally, we apply our results to the electroweak phase transition in the standard model.