Quantum field theory by Ciro Santilli 37 Updated 2025-07-16
Theoretical framework on which quantum field theories are based, theories based on framework include:so basically the entire Standard Model
The basic idea is that there is a field for each particle particle type.
And then those fields interact with some Lagrangian.
One way to look at QFT is to split it into two parts:
Then interwined with those two is the part "OK, how to solve the equations, if they are solvable at all", which is an open problem: Yang-Mills existence and mass gap.
There appear to be two main equivalent formulations of quantum field theory:
Video 1.
Quantum Field Theory visualized by ScienceClic English (2020)
Source. Gives one piece of possibly OK intuition: quantum theories kind of model all possible evolutions of the system at the same time, but with different probabilities. QFT is no different in that aspect.
Video 2.
Quantum Fields: The Real Building Blocks of the Universe by David Tong (2017)
Source. Boring, does not give anything except the usual blabla everyone knows from Googling:
Video 3.
Quantum Field Theory: What is a particle? by Physics Explained (2021)
Source. Gives some high level analogies between high level principles of non-relativistic quantum mechanics and special relativity in to suggest that there is a minimum quanta of a relativistic quantum field.
Gauge theory by Ciro Santilli 37 Updated 2025-07-16
The term and idea was first introduced initialized by Hermann Weyl when he was working on combining electromagnetism and general relativity to formulate Maxwell's equations in curved spacetime in 1918 and published as Gravity and electricity by Hermann Weyl (1918). Based on perception that symmetry implies charge conservation. The same idea was later adapted for quantum electrodynamics, a context in which is has even more impact.
Gauge field by Ciro Santilli 37 Updated 2025-07-16
A random field you add to make something transform locally the way you want. See e.g.: Video "Deriving the qED Lagrangian by Dietterich Labs (2018)".
Gauge symmetry by Ciro Santilli 37 Updated 2025-07-16
Video 1.
Lawrence Krauss explains Gauge symmetry by Joe Rogan (2017)
Source.
While most of this is useless as you would expect from the channel, it does give one key idea: you can change charge locally, but things somehow still work out.
And this has something to do with the general intuition of special relativity that only local measures make much sense, as evidenced by Einstein synchronization.
Fock space by Ciro Santilli 37 Updated 2025-07-16
Yup, this one Focks you up.
Second quantization by Ciro Santilli 37 Updated 2025-07-16
Second quantization also appears to be useful not only for relativistic quantum mechanics, but also for condensed matter physics. The reason is that the basis idea is to use the number occupation basis. This basis is:
Bibliography:
Renormalization by Ciro Santilli 37 Updated 2025-07-16
Video 1.
The Biggest Ideas in the Universe | 11. Renormalization by Sean Carroll (2020)
Source. Gives a very quick and high level overview of renormalization. It is not enough to satisfy Ciro Santilli as usual for other Sean Carroll videos, but it goes some way.
Effective field theory by Ciro Santilli 37 Updated 2025-07-16
www.youtube.com/watch?v=WB8r7CU7clk&list=PLUl4u3cNGP60TvpbO5toEWC8y8w51dtvm by Iain Stewart. Basically starts by explaining how quantum field theory is so generic that it is hard to get any numerical results out of it :-)
But in particular, we want to describe those subtheories in a way that we can reach arbitrary precision of the full theory if desired.
Video 1.
Yang-Mills 1 by David Metzler (2011)
Source.
A bit disappointing, too high level, with very few nuggests that are not Googleable withing 5 minutes.
Breakdown:
Video 2. Source. 2 hour talk at the Kavli Institute for Theoretical Physics. Too mathematical, 2021 Ciro can't make much out of it.
Video 3.
Lorenzo Sadun on the "Yang-Mills and Mass Gap" Millennium problem
. Source. Unknown year. He almost gets there, he's good. Just needed to be a little bit deeper.
Theory that describes electrons and photons really well, and as Feynman puts it "accounts very precisely for all physical phenomena we have ever observed, except for gravity and nuclear physics" ("including the laughter of the crowd" ;-)).
Learning it is one of Ciro Santilli's main intellectual fetishes.
While Ciro acknowledges that QED is intrinsically challenging due to the wide range or requirements (quantum mechanics, special relativity and electromagnetism), Ciro feels that there is a glaring gap in this moneyless market for a learning material that follows the Middle Way as mentioned at: the missing link between basic and advanced. Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) is one of the best attempts so far, but it falls a bit too close to the superficial side of things, if only Feynman hadn't assumed that the audience doesn't know any mathematics...
The funny thing is that when Ciro Santilli's mother retired, learning it (or as she put it: "how photons and electrons interact") was also one of her retirement plans. She is a pharmacist by training, and doesn't know much mathematics, and her English was somewhat limited. Oh, she also wanted to learn how photosynthesis works (possibly not fully understood by science as that time, 2020). Ambitious old lady!!!
Combines special relativity with more classical quantum mechanics, but further generalizing the Dirac equation, which also does that: Dirac equation vs quantum electrodynamics. The name "relativistic" likely doesn't need to appear on the title of QED because Maxwell's equations require special relativity, so just having "electro-" in the title is enough.
Before QED, the most advanced theory was that of the Dirac equation, which was already relativistic but TODO what was missing there exactly?
As summarized at: youtube.com/watch?v=_AZdvtf6hPU?t=305 Quantum Field Theory lecture at the African Summer Theory Institute 1 of 4 by Anthony Zee (2004):
That video also mentions the interesting idea that:Therefore, for small timescales, energy can vary a lot. But mass is equivalent to energy. Therefore, for small time scale, particles can appear and disappear wildly.
QED is the first quantum field theory fully developed. That framework was later extended to also include the weak interaction and strong interaction. As a result, it is perhaps easier to just Google for "Quantum Field Theory" if you want to learn QED, since QFT is more general and has more resources available generally.
Like in more general quantum field theory, there is on field for each particle type. In quantum field theory, there are only two fields to worry about:
Video 1.
Lecture 01 | Overview of Quantum Field Theory by Markus Luty (2013)
Source. This takes quite a direct approach, one cool thing he says is how we have to be careful with adding special relativity to the Schrödinger equation to avoid faster-than-light information.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
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    Screenshot of the "Derivative" topic page
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    Figure 4.
    Visual Studio Code extension tree navigation
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    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
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