Equivalence of Hamiltonian and Lagrangian path integral quantization: Effective gauge theories

The equivalence of correct Hamiltonian and naive Lagrangian (Faddeev-Popov) path integral quantization (Matthews's theorem) is proven for gauge theories with arbitrary effective interaction terms. Effective gauge-boson self-interactions and effective interactions with scalar and fermion fields are considered. This result becomes extended to effective gauge theories with higher derivatives of the fields.