Single twistor description of massless, massive, AdS, and other interacting particles

TL;DR

This paper extends the Penrose twistor transform to a unified framework describing various particles, including massless, massive, and interacting particles, using a single twistor with four complex degrees of freedom.

Contribution

It introduces a unified twistor-based description for diverse particle systems, simplifying previous multi-twistor approaches and covering a broad range of dynamical scenarios.

Findings

Unified twistor description for multiple particle types

Single twistor with four complex degrees of freedom suffices

Simplifies the representation of interacting and curved space particles

Abstract

The Penrose transform between twistors and the phase space of massless particles is generalized from the massless case to an assortment of other particle dynamical systems, including special examples of massless or massive particles, relativistic or non-relativistic, interacting or non-interacting, in flat space or curved spaces. Our unified construction involves always the \it{same} twistor Z^A with only four complex degrees of freedom and subject to the \it{same} helicity constraint. Only the twistor to phase space transform differs from one case to another. Hence a unification of diverse particle dynamical systems is displayed by the fact that they all share the same twistor description. Our single twistor approach seems to be rather different and strikingly economical construction of twistors compared to other past approaches that introduced multiple twistors to represent some similar but far more limited set of particle phase space systems.