The Ward-Takahashi identity in quantum electrodynamics ($QED_4$), first considered by J. C. Ward and Y. Takahashi, correlates the wave function renormalization for the electron to its vertex renormalization function. It guarantees the cancellation of ultraviolet (UV) divergences to all orders of perturbation theory.
Since the QED in the light-front gauge is a constrained theory that brings a more demanding UV renormalization program due to the inevitable non-local terms, we check the Ward-Takahashi identity to the one-loop level, using the Mandelstam-Leibbrandt prescription to handle the characteristic light-front poles that appear in the Feynman integrals. Our calculations for the vertex correction and inverse electron propagators show that the strict light-front part contributions do indeed satisfy the Ward-Takahashi identity to one-loop order.