Thursday, September 17, 2015

Could one realize number theoretical universality for functional integral?

Number theoretical vision relies on the notion of number theoretical universality (NTU). In fermionic sector NTU is necessary: one cannot speak about real and p-adic fermions as separate entities and fermionic anti-commutation relations are indeed number theoretically universal.

By supersymmetry NTU should apply also to functional integral over WCW (or its sector defined by given causal diamond CD) involved with the definition of scattering amplitudes. The expression for the integral should make sense in all number fields simultaneously. At first this condition looks horrible but the Kähler structure of WCW and the identification of vacuum functional as exponent of Kähler function, and the unique adelic properties of Neper number e give excellent hopes about NTU and also predict the general forms of the functional integral and of the value spectrum of Kähler action for preferred extremals.

See the chapter Unified Number Theoretic Vision of "Physics
as Generalized Number Theory" or the article Could one realize number theoretical universality for functional integral?.

For a summary of earlier postings see Links to the latest progress in TGD.

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