Introduction

The purpose of twistor diagram theory remains as first envisaged by Penrose [18]. It is to enable us to identify a new fundamental structure in twistor geometry for the description of quantum field theory (QFT) in flat space-time. This new structure should eliminate the unsatisfactory features of standard QFT, particularly the divergences and renormalisation schemes. The further hope is that a twistor-geometric formalism could explain the spectrum of observed physical particles and provide the starting point for the unification of QFT with gravity.

The essential character of twistor diagram theory also remains Penrose's. The idea is that twistor diagrams themselves are to play the role in a twistorial QFT of Feynman diagrams in conventional QFT. That is, they are to supply a perturbation expansion calculus for physical scattering amplitudes. The guiding principle is that in analogy to Feynman diagrams they should be defined by the systematic combination of very simple elements. These elements and the rules for combining them should be expressible in a form which is essentially combinatorial (hence appropriately represented by a diagrammatic formalism). The elements and the rules should also be manifestly finite. In the original ‘classical’ theory they were also to be manifestly conformally invariant. As such the theory was at first necessarily restricted to the description of massless fields, and indeed was envisaged originally as to be applied to massless quantum electrodynamics (QED).