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+→0 (p+≠0) in the continuum limit. In order to avoid the divergence, we introduce an infrared cutoff function FIR(p,Λ) which is not Lorentz invariant. It is then shown that the gauge boson obtains mass dynamically on the LF.