Duffin–Kemmer–Petiau and Klein–Gordon–Fock equations for electromagnetic, Yang–Mills and external gravitational field interactions: proof of equivalence

Abstract

Starting from the Generating functional for the Green Function (GF), constructed from the Lagrangian action in the Duffin–Kemmer–Petiau (DKP) theory ( L -approach) we strictly prove that the physical matrix elements of the S-matrix in DKP and Klein–Gordon–Fock (KGF) theories coincide in cases of interacting 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 the reduction formulas of Lehmann, Symanzik and Zimmermann (LSZ). We prove that many photons and Yang–Mills particles GF coincide in both theories too.