Zero Modes on the Light Front

TL;DR

This paper discusses the significance of zero modes in light-front field theories, highlighting their impact on numerical convergence, vacuum structure, and resolving quantization discrepancies.

Contribution

It provides a comprehensive survey of zero modes' roles and addresses the critical coupling discrepancy in $ ext{phi}^4_{1+1}$ theory with proper zero mode treatment.

Findings

Zero modes influence convergence and vacuum properties.

Proper zero mode treatment can resolve quantization discrepancies.

Open questions remain in the understanding of zero modes.

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.