Incoming links: Lecture 3
Local symmetries appear to be a synonym to internal symmetry, see description at: Section "Internal and spacetime symmetries".
As mentioned at Quote , local symmetries map to forces in the Standard Model.
Appears to be a synonym for: gauge symmetry.
A local symmetry is a transformation that you apply a different transformation for each point, instead of a single transformation for every point.
TODO what's the point of a local symmetry?
Bibliography:
- lecture 3
- physics.stackexchange.com/questions/48188/local-and-global-symmetries
- www.physics.rutgers.edu/grad/618/lects/localsym.pdf by Joel Shapiro gives one nice high level intuitive idea:
In relativistic physics, global objects are awkward because the finite velocity with which effects can propagate is expressed naturally in terms of local objects. For this reason high energy physics is expressed in terms of a field theory.
- Quora:
- www.youtube.com/watch?v=-_qNKbwM_eE Unsolved: Yang-Mills existence and mass gap by J Knudsen (2019). Gives 10 key points, but the truly hard ones are too quick. He knows the thing though.
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:
- 1 www.youtube.com/watch?v=j3fsPHnrgLg: too basic
- 2 www.youtube.com/watch?v=br6OxCLyqAI?t=569: mentions groups of Lie type in the context of classification of finite simple groups. Each group has a little diagram.
- 3 youtu.be/1baiIxKKQlQ?list=PL613A31A706529585&t=728 the original example of a local symmetry was general relativity, and that in that context it can be clearly seen that the local symmetry is what causes "forces" to appear
- youtu.be/1baiIxKKQlQ?list=PL613A31A706529585&t=933 local symmetry gives a conserved current. In the case of electromagnetism, this is electrical current. This was the only worthwhile thing he sad to 2021 Ciro. Summarized at: local symmetries of the Lagrangian imply conserved currents.
- 4 youtu.be/5ljKcWm7hoU?list=PL613A31A706529585&t=427 electromagnetism has both a global symmetry (special relativity) but also local symmetry, which leads to the conservation of charge current and forces.lecture 3 properly defines a local symmetry in terms of the context of the lagrangian density, and explains that the conservation of currents there is basically the statement of Noether's theorem in that context.
Millennium Prize Problem: Yang Mills Theory by David Gross (2018)
Source. 2 hour talk at the Kavli Institute for Theoretical Physics. Too mathematical, 2021 Ciro can't make much out of it.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.