On Equivalence of Duffin-Kemmer-Petiau and Klein-Gordon Equations

TL;DR

This paper rigorously proves the equivalence of Duffin-Kemmer-Petiau and Klein-Gordon theories for charged scalar particles interacting with electromagnetic fields, using Hamiltonian and Green function formalisms.

Contribution

It provides a detailed Hamiltonian and Green function-based proof of the equivalence between DKP and KG theories for charged scalar particles.

Findings

S-matrix elements are relativistically invariant.

Equivalence holds for interactions with external and quantized electromagnetic fields.

Reduction formulas confirm the theories' equivalence in general conditions.

Abstract

A strict proof of equivalence between Duffin-Kemmer-Petiau (DKP) and Klein-Gordon (KG) theories is presented for physical S-matrix elements in the case of charged scalar particles interacting in minimal way with an external or quantized electromagnetic field. First, Hamiltonian canonical approach to DKP theory is developed in both component and matrix form. The theory is then quantized through the construction of the generating functional for Green functions (GF) and the physical matrix elements of S-matrix are proved to be relativistic invariants. The equivalence between both theories is then proved using the connection between GF and the elements of S-matrix, including the case of only many photons states, and for more general conditions - so called reduction formulas of Lehmann, Symanzik, Zimmermann.