Pauli–Villars regularization consists of introducing a fictitious mass term. For example, we would replace a photon propagator 1 k 2 + i ϵ ϵ , by 1 k 2 + i ϵ ϵ − − 1 k 2 − − Λ Λ 2 + i ϵ ϵ , where Λ Λ can be thought of as the mass of a fictitious heavy photon, whose contribution is subtracted from that of an ordinary photon.