The causal approach proof for the equivalence of $SDKP_{4}$ and $SQED_{4}$ at tree-level

TL;DR

This paper provides a complete causal perturbation theory proof demonstrating the equivalence of scalar quantum electrodynamics and Duffin-Kemmer-Petiau scalar gauge theory at tree level, confirming they yield identical differential cross sections.

Contribution

It offers the first comprehensive causal perturbation theory proof of the equivalence between $SDKP_{4}$ and $SQED_{4}$ at tree level.

Findings

Both formulations produce identical differential cross sections at tree level.

The proof clarifies the theoretical equivalence of the two scalar electromagnetic interaction models.

Abstract

The description of the electromagnetic interaction of charged spinless particles is usually formulated by the Scalar Quantum Electrodynamics. However, there is an alternative formulation given by the Duffin-Kemmer-Petiau theory: the Scalar DKP gauge theory. The proof of the equivalence between these two formulations has been discussed in many researches, but there is not yet a conclusive proof. In this paper, we initiate a complete proof in the framework of the Causal Perturbation theory, showing that both scalar formulations provide the same results for the differential cross section at tree level.