Duffin-Kemmer-Petiau equation on the quaternion field

TL;DR

This paper explores the relationship between the Klein-Gordon and Duffin-Kemmer-Petiau equations on quaternion fields, revealing new equivalences and differences, and discusses potential interpretations of anomalous solutions in quaternion quantum field theory.

Contribution

It demonstrates the equivalence of Klein-Gordon and DKP equations on quaternion fields and introduces new forms of Klein-Gordon equations with distinct properties.

Findings

Klein-Gordon equation on quaternions is equivalent to a pair of DKP equations

New forms of Klein-Gordon equations are derived with notable differences from standard versions

Discussion on interpreting anomalous solutions in quaternion quantum field theory

Abstract

We show that the Klein-Gordon equation on the quaternion field is equivalent to a pair of DKP equations. We shall also prove that this pair of DKP equations can be taken back to a pair of new KG equations. We shall emphasize the important difference between the standard and the new KG equations. We also present some qualitative arguments, concerning the possibility of interpreting anomalous solution, within a quaternion quantum field theory.