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.


Quantum field theory lecture by tobias osborne 2017/lecture 3

ID: quantum-field-theory-lecture-by-tobias-osborne-2017/lecture-3