Corroborating the equivalence between the Duffin-Kemmer-Petiau and the Klein-Gordon and Proca equations

TL;DR

This paper demonstrates the equivalence between the Duffin-Kemmer-Petiau theory and the Klein-Gordon and Proca equations, clarifying electromagnetic coupling issues and addressing misconceptions about Hermiticity.

Contribution

It clarifies the correct physical form of the Duffin-Kemmer-Petiau field and resolves ambiguities in electromagnetic coupling within the theory.

Findings

Source term appears in Hamiltonian form with electromagnetic coupling

Correct physical form removes the source term regardless of matrix representation

Addresses misconceptions about Hermiticity in the DKP theory

Abstract

It is shown that the Hamiltonian version of the Duffin-Kemmer-Petiau theory with electromagnetic coupling brings about a source term at the current. It is also shown that such a source term disappears from the scenario if one uses the correct physical form for the Duffin-Kemmer-Petiau field, regardless the choice for representing the Duffin-Kemmer-Petiau matrices. This result is used to fix the ambiguity in the electromagnetic coupling in the Duffin-Kemmer-Petiau theory. Moreover, some widespread misconceptions about the Hermiticity in the Duffin-Kemmer-Petiau theory are discussed.