Mathematical Physics


$e, \pi, \chi \cdots \alpha?$

Authors: Lucian M Ionescu

Feynman amplitudes are periods, and also coefficients of the QED partition function with a formal deformation parameter the fine structure constant $\alpha$. Moreover, this truly fundamental mathematical constant is the ratio of magnetic (fluxon) vs. electric charge, as well as the grading of the decay lifetimes telling apart weak from strong ``interactions''. On the other (Mathematical) hand $e$ is the ``inverse'' of $\pi$, another deformation parameter (no ordinary period), as Euler's famous identity $exp(2\pi i)=1$ suggests. In a recent work, Atiyah related $\alpha$ and the Todd function. But Todd classes are inverses of Chern classes, suggesting further ``clues'' to look for conceptual relationships between these mathematical constants, in an attempt to catch a a Platonic and Exceptional Universe by the TOE.

Comments: 30 Pages.

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Submission history

[v1] 2019-12-19 13:40:49

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