where:
- is the electromagnetic tensor
Note that this is the sum of the:Note that the relationship between and is not explicit. However, if we knew what type of particle we were talking about, e.g. electron, then the knowledge of psi would also give the charge distribution and therefore
- Dirac Lagrangian, which only describes the "inertia of bodies" part of the equation
- the electromagnetic interaction term , which describes term describes forces
As mentioned at the beginning of Quantum Field Theory lecture notes by David Tong (2007):
- by "Lagrangian" we mean Lagrangian density
- the generalized coordinates of the Lagrangian are fields
Does the exact position of vertices matter in Feynman diagrams? by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16What they presented on richard Feynman's first seminar in 1941. Does not include quantum mechanics it seems.
This is quite mind blowing. The laws of physics actually differentiate between particles and antiparticles moving in opposite directions!!!
Only the weak interaction however does it of the fundamental interactions.
Some historical remarks on Surely You're Joking, Mr. Feynman section "The 7 Percent Solution".
It gets worse of course with CP Violation.
Initially a phenomenological guess to explain the periodic table. Later it was apparently proven properly with the spin-statistics theorem, physics.stackexchange.com/questions/360140/theoretical-proof-of-paulis-exclusion-principle.
And it was understood more and more that basically this is what prevents solids from collapsing into a single nucleus, not electrical repulsion: electron degeneracy pressure!
Bibliography:
- www.youtube.com/watch?v=EK_6OzZAh5k How Electron Spin Makes Matter Possible by PBS Space Time (2021)
The different only shows up for field, not with particles. For fields, there are two types of changes that we can make that can keep the Lagrangian unchanged as mentioned at Physics from Symmetry by Jakob Schwichtenberg (2015) chapter "4.5.2 Noether's Theorem for Field Theories - Spacetime":
- spacetime symmetry: act with the Poincaré group on the Four-vector spacetime inputs of the field itself, i.e. transforming into
- internal symmetry: act on the output of the field, i.e.:
From the spacetime theory alone, we can derive the Lagrangian for the free theories for each spin:Then the internal symmetries are what add the interaction part of the Lagrangian, which then completes the Standard Model Lagrangian.
Free to view draft: web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf Page presenting it: web.physics.ucsb.edu/~mark/qft.html
Number of pages: 616!
Don't redistribute clause, and final version by Cambridge University Press, alas, so corrections will never be merged back: web.physics.ucsb.edu/~mark/qft.html. But at least he's collecing erratas for the published (and therefore draft) versions there.
The preface states that one of its pedagogical philosophies is to "Illustration of the basic concepts with the simplest examples.", so maybe there is hope after all.
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 3 by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16- symmetry in classical field theory
- from Lagrangian density we can algorithmically get equations of motion, but the Lagrangian density is a more compact way of representing the equations of motion
- definition of symmetry in context: keeps Lagrangian unchanged up to a total derivative
- Noether's theorem
- youtu.be/cj-QpsZsDDY?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=3062 Lagrangian and conservation example under translations
- youtu.be/cj-QpsZsDDY?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=3394 same but for Poincaré transformations But now things are harder, because it is harder to describe general infinitesimal Poincare transforms than it was to describe the translations. Using constraints/definition of Lorentz transforms, also constricts the allowed infinitesimal symmetries to 6 independent parameters
- youtu.be/cj-QpsZsDDY?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=4525 brings out Poisson brackets, and concludes that each conserved current maps to a generator of the Lie algebra
Looks interesting.
It seems to abstract the part about the client messaging the backend, which focuses on being able to easily plug in a number of Front-end web framework to manage client state.
Uses Socket.IO, which allows the client Javascript to register callbacks when data is updated to achieve Socket.IO, e.g. their default chat app does:so that message appear immediately as they are sent.
client.service('messages').on('created', addMessage);Their standard template from But it is in itself a completely boring app with a single splash page, and no database interaction, so not a good showcase. The actual showcase app is feathersjs/feathers-chat.
feathers generate app on @feathersjs/cli@4.5.0 includes:which looks promising! They don't have a default template for a Front-end web framework however unfortunately: docs.feathersjs.com/guides/frameworks.html#the-feathers-chat lists a few chat app versions, which is their hello world:
- Front-end web framework: not built-in on generator, but there are some sample repos pointed from the documentation, and they did work out-of-box:
And there is no official example of the chat app that is immediately deployable to Heroku: FeathersJS Heroku deployment, all setups require thinking.
Pinned article: Introduction to the OurBigBook Project
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Intro to OurBigBook
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Figure 3. Visual Studio Code extension installation.
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