The Ward-Takahashi identity in QED is q_μ M^μ = 0: when the photon polarization vector ε^μ is replaced by its momentum q^μ, the amplitude vanishes. This is the quantum field-theoretic expression of current conservation ∂_μ j^μ = 0, and follows directly from U(1) gauge invariance. It implies that the longitudinal photon polarization decouples from all physical processes, ensuring only 2 transverse photon degrees of freedom contribute. Ward identities also relate the vertex function Γ^μ to the full propagator: q_μ Γ^μ(p+q, p) = S⁻¹(p+q) − S⁻¹(p), constraining renormalization at all orders.