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This form is not really an inner product in the common modern definition, because it is not positive definite, only a symmetric bilinear form.
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What does it mean that photons are force carriers for electromagnetism? Updated 2025-07-16
TODO find/create decent answer.
I think the best answer is something along:
- local symmetries of the Lagrangian imply conserved currents. gives conserved charges.
- OK now. We want a local symmetry. And we also want:Given all of that, the most obvious and direct thing we reach a guess at the quantum electrodynamics Lagrangian is Video "Deriving the qED Lagrangian by Dietterich Labs (2018)"
- Dirac equation: quantum relativistic Newton's laws that specify what forces do to the fields
- electromagnetism: specifies what causes forces based on currents. But not what it does to masses.
A basic non-precise intuition is that a good model of reality is that electrons do not "interact with one another directly via the electromagnetic field".
A better model happens to be the quantum field theory view that the electromagnetic field interacts with the photon field but not directly with itself, and then the photon field interacts with parts of the electromagnetic field further away.
The more precise statement is that the photon field is a gauge field of the electromagnetic force under local U(1) symmetry, which is described by a Lie group. TODO understand.
This idea was first applied in general relativity, where Einstein understood that the "force of gravity" can be understood just in terms of symmetry and curvature of space. This was later applied o quantum electrodynamics and the entire Standard Model.
From Video "Lorenzo Sadun on the "Yang-Mills and Mass Gap" Millennium problem":
- www.youtube.com/watch?v=pCQ9GIqpGBI&t=1663s mentions this idea first came about from Hermann Weyl.
- youtu.be/pCQ9GIqpGBI?t=2827 mentions that in that case the curvature is given by the electromagnetic tensor.
Bibliography:
- www.youtube.com/watch?v=qtf6U3FfDNQ Symmetry and Quantum Electrodynamics (The Standard Model Part 1) by ZAP Physics (2021)
- www.youtube.com/watch?v=OQF7kkWjVWM The Symmetry and Simplicity of the Laws of Nature and the Higgs Boson by Juan Maldacena (2012). Meh, also too basic.
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Quantum electrodynamics bibliography Updated 2025-07-16
fafnir.phyast.pitt.edu/py3765/ Phys3765 Advanced Quantum Mechanics -- QFT-I Fall 2012 by E.S. Swanson mentions several milestone texts including:
Year On Updated 2025-07-16
Birch and Swinnerton-Dyer conjecture in two minutes by Ciro Santilli Updated 2025-07-16
Summary:
- overview of the formula of the BSD conjecture
- definition of elliptic curve
- domain of an elliptic curve. Prerequisite: field
- elliptic curve group. Prerequisite: group
- Mordell's theorem lets us define the rank of an elliptic curve over the rational numbers, which is the . Prerequisite: generating set of a group
- reduction of an elliptic curve from to lets us define as the number of elements of the generated finite group
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Michael J. Saylor Updated 2025-07-16
- twitter.com/saylor 2.6 M followers as of 2022. Because of Bitcoin? Or was he famous before that?
- www.michael.com/ yes, he is Michael.com lol. When did he get the domain, and at what price? He's mildlly obsessed with domain names it seems: www.domainsherpa.com/saylor/. He also bought
frank.com,mike.com.emma.com. This was between 1994 and 2000. He mentions that his email issaylor@strategy.com.strategy.comredirects tomicrostrategy.comas of 2022, so seems still valid.We actually got a backlink from tvt.phishlabs.com to this page in August 2022, a phising security provider, presumably for showing his email here. This reminds Ciro of the All GitHub Commit Emails event!A quick google for that address also leads to www.washingtonpost.com/wp-srv/liveonline/00/business/saylor0621.htm, a year 2000 profile page by the Washington Post, followed by a Q&A. In the Q&A, Michael himself gives his email in relation to Saylor Academy:so it was already beyond leaked. Ciro did hit that email address seeking funding for OurBigBook.com, but no reply unfortunately. Maybe you gotta be part of the Rockefeller family to get a reply from these people? Well, at least this led to Ciro learning about the Rockefeller Foundation.Kensington, Maryland: What has happened to your vision of an internet university? I believe it is an important initiative and it doesn't require $100 million to get started. We at the Rockefeller Foundation would like to become involved. How can we do this?Michael Saylor: The internet university is alive and well. My goal is to initially roll out a cyber-libary of digital video that can be used by any for-profit or non-profit organization in order to accelerate the free education initiative. Eventually, people may just go direct to the web site.
Optical component Updated 2025-07-16
There are unlisted articles, also show them or only show them.