A no-go theorem for the $n$-twistor description of a massive particle

TL;DR

The paper proves that a genuine n-twistor description of a massive particle in four-dimensional Minkowski space cannot exist for n≥3, as it reduces to simpler twistor descriptions.

Contribution

It establishes a no-go theorem showing the limitations of n-twistor formulations for massive particles in four-dimensional spacetime.

Findings

n-twistor expression reduces to two-twistor form for massive particles

n-twistor description is equivalent to one- or two-twistor descriptions

Genuine n-twistor description fails for n≥3

Abstract

It is proved that the $n$-twistor expression of a particle's four-momentum vector reduces, by a unitary transformation, to the two-twistor expression for a massive particle or the one-twistor expression for a massless particle. Therefore the {\em genuine} $n$-twistor description of a massive particle in four-dimensional Minkowski space fails for the case $n\ge3$.