Equivalence of the Duffin–Kemmer–Petiau and Klein–Gordon–Fock equations

A strict proof of the equivalence of the Duffin–Kemmer–Petiau and Klein–Gordon–Fock theories is presented for physical $S$-matrix elements in the case of charged scalar particles minimally interacting with an external or quantized electromagnetic field. The Hamiltonian canonical approach to the Duffin–Kemmer–Petiau theory is first developed in both the component and the matrix form. The theory is then quantized through the construction of the generating functional for the Green's functions, and the physical matrix elements of the $S$-matrix are proved to be relativistic invariants. The equivalence of the two theories is then proved for the matrix elements of the scattered scalar particles using the reduction formulas of Lehmann, Symanzik, and Zimmermann and for the many-photon Green's functions.