Differential algebra of biquaternions. 4. Twistor and twistors fields

TL;DR

This paper develops a biquaternionic framework for wave equations, constructing solutions that describe various types of twistors and analyzing their energy properties within a differential algebra setting.

Contribution

It introduces a novel biquaternionic approach to wave equations and explicitly constructs solutions for nonstationary, time-harmonic, and static twistors.

Findings

Constructed generalized solutions for biquaternionic wave equations

Determined elementary harmonic twistors and their energy biquaternions

Built polarized and unpolarized twistors fields

Abstract

On base of differential biquaternions algebra and generalized functions theory the biquaternionic wave equation is considered under vector representation of its structural coefficient. Its generalized solutions are constructed, which describe nonstationary, time-harmonic and static twistors. Elementary harmohic twistors are determined, their biquaternions of energy-inpulse are calculated. By use of them polorized and unpolarized twistors field have been constructed.