= Lecture 3
https://www.youtube.com/watch?v=cj-QpsZsDDY&list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&index=3
* 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>
* https://youtu.be/cj-QpsZsDDY?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=3062 Lagrangian and conservation example under translations
* https://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
* https://youtu.be/cj-QpsZsDDY?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=4525 brings out <Poisson brackets>, and concludes that each conserved current maps to a <generator of a Lie algebra>[generator of the Lie algebra]
This allows you to build the symmetry back from the conserved charges, just as you can determine conserved charges starting from the symmetry.