MPI H-V19-1997 DPNU-97-22 hep-th/9704171 Zero Mode and Symmetry Breaking on the Light Front

We study the zero mode and the spontaneous symmetry breaking on the light front. We use the discretized light-cone quantization a la Maskawa-Yamawaki to treat the zero mode in a clean separation from all other modes. It is then shown that the Nambu-Goldstone (NG) phase can be realized on the trivial light-front vacuum only when an explicit symmetry-breaking mass of the NG boson m is introduced. The NG-boson zero mode integrated over the light front must exhibit singular behavior 1=m2 in the symmetric limit m ! 0, which implies that current conservation is violated at zero mode, or equivalently the light-front charge is not conserved even in the symmetric limit. We demonstrate this peculiarity in a concrete model, the linear sigma model, where the role of zero-mode constraint is clari ed. We nally compare our result with the continuum theory. It is shown that in the continuum theory it is di cult to remove the zero mode which is not a single mode with measure zero but the accumulating point causing uncontrollable infrared singularity. A possible way out within the continuum theory is also suggested. 1 E-mail address: [email protected] 2 E-mail address: [email protected]