Four-divergence as a paravector operator. Invariance of the wave equation under orthogonal paravector transformation

TL;DR

This paper demonstrates that the wave equation remains invariant under orthogonal paravector transformations by deriving four identities involving the four-divergence operator and analyzing their implications for reference frame rotations.

Contribution

It introduces four identities involving four-divergence and proves the invariance of the wave equation under orthogonal paravector transformations, extending understanding of spacetime symmetries.

Findings

Wave equation invariance under orthogonal paravector transformations

Derived four identities involving four-divergence

Transformation rules for spatio-temporal operators under rotation

Abstract

The article presents four identities containing the spatio-temporal differential operator also known as four-divergence. These equations are used to prove the invariance of wave equation under orthogonal paravector transformations. Moreover, the transformation of equations containing spatio-temporal differential operators under the rotation of reference frame has been presented.