Should one replace the notion of unitary matrix with Kaehler metric of fermionic state space?

The article about construction of twistor amplitudes is quite near to its “final” form.

Many new ideas deepening the views about M⁸-H duality, adelic physics, zero energy ontology and about the interpretation of quantum theory itself emerged.

In particular, it became clear that quantum TGD is not encoded by unitary S-matrix, which is highly ad hoc non-relativistic notion and leads to difficulties in twistor approach and also in TGD, but by Kaehler metric for WCW extended to include also fermion sector as a kind of analogs of super-space. This leads to a more general view about state: in TGD state is analogous to thermodynamic state as square root of it and scattering amplitudes characterize it and is parametrized by complex coordinates of the fermionic state space in a manner bringing in mind coherent states.

The fermionic Hilbert space becomes Kaehler geometry which by its infinite-dimensionality has constant curvature and maximal symmetries possessed by scattering amplitudes between zero energy states defining the K”ahler metric. Physics is unique from its existence.

Fermionic part of the Kahler metric codes for the transition amplitudes and probabilities as I realized already years ago and wrote an article about it (see this) but did not dare to take the idea completely seriously since the transition probabilities also contained imaginary parts although probability conservation was true for their real parts. What could be the interpretation of the imaginary parts?

The identification of the Kaehler metric with the Fisher information matrix resolved my suspicions. The probability interpretation is only one facet of a more general view. In the new “eastern” view, the ensemble for a square root of thermodynamics is not formed by particles but by transitions in accordance with zero energy ontology, where 4-D time evolution rather than 3-D state is the fundamental entity.

See the article About TGD counterparts of twistor amplitudes or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.