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Gospel of Matthew 7:13:
Enter through the narrow gate. For wide is the gate and broad is the road that leads to destruction, and many enter through it.
Ciro Santilli really likes this one, because he feels that where many people go, it is useless to go again. It is much better to explore that which few can do, but which many will need.
Lecture notes found by Googling "quantum field theory pdf":
- www.ppd.stfc.ac.uk/Pages/Dasgupta_08_Intro_to_QFT.pdf "An Introduction to Quantum Field Theory" by Mrinal Dasgupta from the University of Manchester (2008). 48 pages.
- www.thphys.uni-heidelberg.de/~weigand/QFT2-14/SkriptQFT2.pdf "Quantum Field Theory I + II" by Timo Weigand from the Heidelberg University. Unknown year, references up to 2008.
- edu.itp.phys.ethz.ch/hs12/qft1/ Quantum Field Theory 1 by Niklas Beisert
- 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
This theorem roughly states that states that for every quantum algorithm, once we reach a certain level of physical error rate small enough (where small enough is algorithm dependant), then we can perfectly error correct.
This algorithm provides the conceptual division between noisy intermediate-scale quantum era and post-NISQ.
Experiments explained by QED but not by the Dirac equation:
- Lamb shift: by far the most famous one
- hyperfine structure TODO confirm
- anomalous magnetic dipole moment of the electron
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
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.
I think they are a tool to calculate the probability of different types of particle decays and particle collision outcomes. TODO Minimal example of that.
And they can be derived from a more complete quantum electrodynamics formulation via perturbation theory.
At Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979), an intuitive explanation of them in termes of sum of products of propagators is given.
- www.youtube.com/watch?v=fG52mXN-uWI The Secrets of Feynman Diagrams | Space Time by PBS Space Time (2017)
What they presented on richard Feynman's first seminar in 1941. Does not include quantum mechanics it seems.
fafnir.phyast.pitt.edu/py3765/ Phys3765 Advanced Quantum Mechanics -- QFT-I Fall 2012 by E.S. Swanson mentions several milestone texts including:
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