Infrared divergence on the light-front and dynamical Higgs mechanism

Dynamical Higgs mechanism on the light-front (LF) is studied using a (1+1) dimensional model, with emphasis on the infrared divergence problem. The consideration of the zero mode $k^+ = 0$ is not sufficient for investigating dynamical symmetry breaking on the LF. It also needs to treat properly an infrared divergence caused by internal momentum $p^+ \to 0 ~ (p^+ \neq 0)$ in the continuum limit. In order to avoid the divergence, we introduce an infrared cutoff function $F_{\rm IR} (p, \Lambda)$ which is not Lorentz invariant. It is then shown that the gauge boson obtains mass dynamically on the LF.