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Quantum field theory lecture by Tobias Osborne (2017) Lecture 3 Updated 2025-07-11 +Created 1970-01-01
- 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
- prokaryote models:
- E. Coli: the most well studied
- mycoplasma: a very minimal genus, notable species: Mycoplasma genitalium
- eukaryote
- S. cerevisiae: simplest eukaryote model. Unicellular.
- C. elegans: simplest multicellular organism model
- vertebrate:
- Zebrafish: simplest vertebrate model
- mammal:
- Mus musculus: simplest mammal model
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