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

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.