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
- 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
The mandatory xkcd: xkcd 927: Standards.
Of course, "Ciro Santilli" with quotes, since all of those are either taken directly from others, or had been previously formulated by others.
Some anecdotes.
Ciro Santilli never splits up functions unless there is more than one calling point. If you split early, the chances that the interface will be wrong are huge, and a much larger refactoring follows.
int cross_block_var;
// First step.
{
int myvar;
}
// Second step.
{
int myvar;
}Ciro has seen and had to deal with in his lifetime with two projects that had like 3 to 10 git separate Git repositories, all created and maintained by the same small group of developers of the same organization, even though one could not build without the other. Keeping everything in sync was Hell! Why not just have three directories inside a single repository with a single source of truth?
Another important case: Linux should have at least a C standard library, init system, and shell in-tree, like BSD Operating Systems, as mentioned at: Section "Linux".
Pinned article: Introduction to the OurBigBook Project
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