What does it mean that photons are force carriers for electromagnetism? by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16TODO 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.
This is a bit "formal hocus pocus first, action later". But withing that category, it is just barely basic enough that 2021 Ciro can understand something.
By: Tobias J. Osborne.
Lecture notes transcribed by a student: github.com/avstjohn/qft
18 1h30 lectures.
Followup course: Advanced quantum field theory lecture by Tobias Osborne (2017).
Quantum field theory lecture by Tobias Osborne (2017) Lecture 4 by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16- quantization. Uses a more or less standard way to guess the quantized system from the classical one using Hamiltonian mechanics.
- youtu.be/fnMcaq6QqTY?t=1179 remembers how to solve the non-field quantum harmonic oscillator
- youtu.be/fnMcaq6QqTY?t=2008 puts hats on everything to make the field version of things. With the Klein-Gordon equation Hamiltonian, everything is analogous to the harmonic oscilator
- web.archive.org/web/20150623011722/http://users.physik.fu-berlin.de/~kleinert/b6/psfiles/qft.pdf by Hagen Kleinert (2015). 1500 pages!
- The Quantum Theory of Fields by Steven Weinberg (2013) www.cambridge.org/core/books/quantum-theory-of-fields/22986119910BF6A2EFE42684801A3BDF
- Quantum Field Theory by Lewis H. Ryder 2nd edition (1996) www.amazon.co.uk/Quantum-Field-Theory-Lewis-Ryder/dp/0521478146
- Lectures of Quantum Field Theory by Ashok Das (2018) www.amazon.co.uk/Lectures-Quantum-Field-Theory-Ashok-ebook/dp/B07CL8Y3KY
- A Modern Introduction to Quantum Field Theory by Michele Maggiore (2005) www.amazon.co.uk/Modern-Introduction-Quantum-Theory-Physics/dp/0198520743
Quantum Field Theory for The Gifted Amateur by Tom Lancaster (2015) by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Gun-type fission weapons are the simplest approach and they work with Uranium-235 bombs as you can ignite it with just one explosion.
But Gun-type fission weapons don't work with plutonium, and weapon grade Plutonium is cheaper than weapon grade Uranium, so it wasn't much used.
Derived from classical first principles, matches Planck's law for low frequencies, but diverges at higher frequencies.
Toy model of matter that exhibits phase transition in dimension 2 and greater. It does not provide numerically exact results by itself, but can serve as a tool to theorize existing and new phase transitions.
As mentioned at: stanford.edu/~jeffjar/statmech/intro4.html some systems which can be seen as modelled by it include:
- the spins direction (up or down) of atoms in a magnet, which can undergo phase transitions depending on temperature as that characterized by the Curie temperature and an externally applied magnetic fieldNeighboring spins like to align, which lowers the total system energy.
- the type of atom at a lattice point in a 2-metal alloy, e.g. Fe-C (e.g. steel). TODO: intuition for the neighbor interaction? What likes to be with what? And aren't different phases in different crystal structures?
Also has some funky relations to renormalization TODO.
Bibliography:
The Ising Model in Python by Mr. P Solver
. Source. The dude is crushing it on a Jupyter Notebook.The type of laser described at: Video "How Lasers Work by Scientized (2017)", notably youtu.be/_JOchLyNO_w?t=581. Mentioned at: youtu.be/_JOchLyNO_w?t=759 That point also mentions that 4-level lasers also exist and are more efficient. TODO dominance? Alternatives?
Three-level laser system by Dr. Nissar Ahmad (2021)
Source. Bibliography:
Computational physics is a good way to get valuable intuition about the key equations of physics, and train your numerical analysis skills:
- classical mechanics
- "Real-time heat equation OpenGL visualization with interactive mouse cursor using relaxation method" under the best articles by Ciro Articles
- phet.colorado.edu PhET simulations from University of Colorado Boulder
Other child sections:
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