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

TL;DR

This paper rigorously proves the equivalence of the Duffin-Kemmer-Petiau and Klein-Gordon-Fock theories for spin-zero particles interacting with electromagnetic, Yang-Mills, and gravitational fields, using generating functionals and LSZ reduction.

Contribution

It provides a strict proof of the equivalence of DKP and KGF theories for various interactions, including external and quantized fields, using a generating functional approach.

Findings

Physical S-matrix elements coincide in DKP and KGF theories.

Green functions for many photons and Yang-Mills particles are identical in both theories.

The proof covers interactions with electromagnetic, Yang-Mills, and gravitational fields.

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.