What's the state of the art of Galois Duality theory over general fields?

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James F Peters Popular answer

This is a great question.

Galois duality theory (also, wtih an ontologic interpretation, Galois-Grathendieck duality) is introduced formally in detail in Section 2 in

https://www.researchgate.net/publication/270564717_Towards_a_Galoisian_Interpretation_of_Heisenberg_Indeterminacy_Principle

See Section 3 for a harmonic interpretation of Galois duality. However, Tate is not mentioned.

An advanced study of duality (including Galois duality) is given in

https://arxiv.org/pdf/1305.0058.pdf

Article Towards a Galoisian Interpretation of Heisenberg Indetermina...

James F Peters

Juan Weisz

I could never dream of going so mathematical with the uncertainty principle.

A Gaussian function (in direct and dual spce) is what minimizes the inequality