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The equivalence of correct Hamiltonian and naive Lagrangian (Faddeev--Popov)path integral quantization (Matthews's theorem) is proven for gauge theorieswith arbitrary effective interaction terms. Effective gauge-bosonself-interactions and effective interactions with scalar and fermion fields areconsidered. This result becomes extended to effective gauge theories withhigher derivatives of the fields.Comment: 14 pages LaTeX, BI-TP 93/40, August 199

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