## Classical TGD and imbedding space twistors
The understanding of twistor structure of imbedding space and its relationship to the consctruction of extremals of Kähler action is certainly greatest breakthroughs in the mathematical understanding of TGD for years. One can say that the good physics provided by TGD can be now combined with the marvelous mathematics produced by string theorists by replacing Calabi-Yau manifolds with twistor spaces assignable to space-time surfaces and representable as sub-manifolds of the twistor space CP Below is the introduction of the article article Classical part of twistor story. I will later add some key pieces of the article.
Twistor Grassmannian formalism has made a breakthrough in
The Cartesian product of twistor spaces CP
In the following I summarize the background and develop a proposal for how to construct extremals of Kähler action in terms of the generalized twistor structure. One ends up with a scenario in which space-time surfaces are lifted to twistor spaces by adding CP There is also a very close analogy with superstring models. Twistor spaces replace Calabi-Yau manifolds and the modification recipe for Calabi-Yau manifolds by removal of singularities can be applied to remove self-intersections of twistor spaces and mirror symmetry emerges naturally. The overall important implication is that the methods of algebraic geometry used in super-string theories should apply in TGD framework. The basic problem of TGD has been indeed the lack of existing mathematical methods to realize quantitatively the view about space-time as 4-surface.
The physical interpretation is totally different in TGD. Twistor space has space-time as base-space rather than forming with it Cartesian factors of a 10-D space-time. The Calabi-Yau landscape is replaced with the space of twistor spaces of space-time surfaces having interpretation as generalized Feynman diagrams and twistor spaces as sub-manifolds of CP For background see the new chapter Classical part of twistor story or the article Classical part of twistor story. |