*This is the tenth episode of the RH Saga.*
The magnetic moment of the electron is one of the fundamental constants of nature that can be predicted by quantum field theory. Quite surprisingly, the Feynman diagram computations of QFT give rise to expressions involving special values of L-functions, and more general periods. We are only beginning to scratch the surface of these connections between physics and number theory. Diving deeper into these mysteries, we may also hope to find some further clues in the search for a geometry over the field with one element.
The overall aim of RH Saga Season 1 is to map the landscape of L-functions, as a foundation for in-depth exploration of some of the most immortal math problems of all time.
*This video is part of a PeakMath project.* Support future PeakMath projects here: https://ko-fi.com/peakmath
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*Chapters:*
00:00 - Intro
01:11 - Table of contents
01:28 - Magnetic moment of the electron
11:00 - Feynman amplitudes
16:02 - Clues for F1
23:09 - Final remarks
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*Links:*
1. Fan, Myers, Sukra, and Gabrielse: Measurement of the Electron Magnetic Moment (2022):
https://arxiv.org/pdf/2209.13084
2. Broadhurst and Roberts: Quadratic relations between Feynman integrals:
https://static1.squarespace.com/static/577da80de3df288b496f8cf7/t/5b8cc87aaa4a99a498331122/1535953018616/BroadhurstRoberts.pdf
3. Aoyama, Kinoshita, and Nio: Theory of the Anomalous Magnetic Moment of the Electron:
https://www.mdpi.com/2218-2004/7/1/28
4. Harvard's Arithmetic Quantum Field Theory Program:
https://cmsa.fas.harvard.edu/event/aqft2024/
5. Francis Brown talk slides: Periods and Cosmic Galois group:
https://www.ihes.fr/~brown/SMFBrown.pdf
6. Francis Brown talk slides from CERN, on mixed L-functions:
https://indico.cern.ch/event/927781/contributions/3926291/attachments/2101487/3533016/EllipticConf.pdf
7. Freeman Dyson's talk on Birds and Frogs:
https://www.ams.org/notices/200902/rtx090200212p.pdf
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*Errata:*
No errors found yet.
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