Duffin-Kemmer-Petiau and Klein-Gordon-Fock Equations for Electromagnetic, Yang-Mills and external Gravitational Field Interactions: proof of equivalence

Abstract

Starting from Generating functional for Green Function (GF), constracted from Lagrangian action in Duffin-Kemmer-Petiau (DKP) theory (L-approach) we strictly prove that the physical matrix elements of S-matrix in DKP and Klein-Gordon-Fock (KGF) theories coincide in cases of interaction spin O particles with external and quantized Maxwell and Yang-Mills fields and in case of external gravitational field (without or with torsion). For the proof we use reduction formulas of Lehmann Symanzik, Zimmermann (LSZ). We prove that many photons and Yang-Mills particles GF coincide in the both theories, too.