Zero Modes on the Light Front

Abstract: Modes with zero longitudinal light-front momentum (zero modes) do have roles to play in the analysis of light-front field theories. These range from improvements in convergence for numerical calculations to implications for the light-front vacuum and beyond to fundamental issues in the connection with equal-time quantization. In particular, the discrepancy in values of the critical coupling for $\phi^4_{1+1}$ theory, between equal-time and light-front quantizations, would appear to be resolvable with the proper treatment of zero modes and near-zero modes. We provide a survey of these issues and point to open questions.