$k^+=0$ Modes in Light-Cone Quantization

TL;DR

This paper studies the role of zero modes in light-cone quantized $ ext{phi}^3$ theory in 1+1 dimensions, demonstrating that zero modes propagate in Feynman diagrams and restore Lorentz invariance.

Contribution

It provides a detailed analysis of the $k^+=0$ mode in light-cone quantization, showing its propagation and impact on Lorentz invariance restoration.

Findings

Zero modes propagate along internal lines in Feynman diagrams.

Light-cone quantization with zero modes recovers Lorentz invariance.

The approach handles the second-class constraint associated with $k^+=0$.

Abstract

We investigate the light-cone quantization of $\phi^3$ theory in 1+1 dimensions with a regularization of discretized light-cone momentum $k^+$. Solving a second-class constraint associated with the $k^+=0$ mode, we show that the $k^+=0$ mode propagates along the internal lines of Feynman diagrams in any order of perturbation, hence our theory recovers the Lorentz invariance.