From Duffin-Kemmer-Petiau to Tzou algebras in relativistic wave equations

TL;DR

This paper explores the connection between Duffin-Kemmer-Petiau and Tzou algebras in relativistic wave equations, demonstrating how higher-dimensional algebras can be reduced to lower-dimensional ones through similarity transformations.

Contribution

It establishes a mathematical relationship between two algebraic frameworks used in relativistic wave equations and provides explicit reduction methods.

Findings

Reduced 5D Duffin-Kemmer-Petiau algebra to 3D Tzou algebra

Reduced 10D Duffin-Kemmer-Petiau algebra to 7D Tzou algebra

Demonstrated similarity transformations between the algebras

Abstract

We study relation between the Duffin-Kemmer-Petiau algebras and some representations of Tzou algebras. Working in the setting of relativistic wave equations we reduce, via a similarity transformation, five and ten dimensional Duffin-Kemmer-Petiau algebras to three and seven dimensional Tzou algebras, respectively.