Introduction

Background and motivations

1. Basic results and problems of twistor approach

2. Results about twistors relevant for TGD

3. Basic definitions related to twistor spaces

4. Why twistor spaces with Kähler structure?

About the identification of 6-D twistor spaces as sub-manifolds of 12-D twistor space

1. Conditions for twistor spaces as sub-manifolds

2. Twistor spaces by adding CP₁ fiber to space-time surfaces

3. Twistor spaces as analogs of Calabi-Yau spaces of super string models

Witten's twistor string approach and TGD

1. Basic ideas about twistorialization of TGD

2. The emergence of the fundamental 4-fermion vertex and of boson exchanges

3. What about SUSY in TGD?

4. What does one really mean with the induction of imbedding space spinors?

5. About the twistorial description of light-likeness in 8-D sense using octonionic spinors

6. How to generalize Witten's twistor string theory to TGD framework?

7. Yangian symmetry

8. Does BCFW recursion have counterpart in TGD?

9. Possible connections of TGD approach with the twistor Grassmannian approach

10. Permutations, braidings, and amplitudes

Could the Universe be doing Yangian arithmetics?

1. Do scattering amplitudes represent quantal algebraic manipulations?

2. Generalized Feynman diagram as shortest possible algebraic manipulation connecting initial and final algebraic objects

3. This was not the whole story yet

From Principles To Diagrams

1. Some mathematical background

2. Surprise: twistorial dynamics does not reduce to a trivial reformulation of the dynamics of Kähler action

3. Basic principles behind construction of amplitudes

Some mathematical details about Grasmannian formalism

1. Yangian algebra and its super counterpart

2. Twistors and momentum twistors and super-symmetrization

3. Brief summary of the work of Arkani-Hamed and collaborators

4. The general form of Grassmannian integrals

5. Canonical operations for Yangian invariants

6. Explicit formulation for recursion relation