Extended geometry and kinematics induced by biquaternionic and twistor structures

TL;DR

This paper explores how biquaternionic algebra and twistor structures extend and influence the geometry and kinematics of space-time, revealing new restrictions on particle-like formations within this framework.

Contribution

It introduces a novel connection between biquaternionic analysis, twistor theory, and extended space-time geometry, highlighting their combined impact on particle transport restrictions.

Findings

Biquaternionic algebra induces an extended space-time geometry.

Twistor structures naturally emerge in biquaternionic analysis.

Rigid restrictions on the transport of singular points are identified.

Abstract

The algebra of biquaternions possess a manifestly Lorentz invariant form and induces an extended space-time geometry. We consider the links between this complex pre-geometry and real geometry of the Minkowski space-time. Twistor structures naturally arise in the framework of biquaternionic analysis. Both together, algebraic and twistor structures impose rigid restriction on the transport of singular points of biquaternion-valued fields identified with particle-like formations.