Ciro Santilli
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For every continuous symmetry in the system (Lie group), there is a corresponding conservation law.
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Furthermore, given the symmetry, we can calculate the derived conservation law, and vice versa.
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As mentioned at http://buzzard.ups.edu/courses/2017spring/projects/schumann-lie-group-ups-434-2017.pdf, what the symmetry (Lie group) acts on (obviously?!) are the Lagrangian generalized coordinates. And from that, we immediately guess that manifolds are going to be important, because the generalized variables of the Lagrangian can trivially be non-Euclidian, e.g. the pendulum lives on an infinite cylinder.
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Video 97. "The most beautiful idea in physics - Noether's Theorem" by Looking Glass Universe (2015) Source. One sentence stands out: the generated quantities are called the generators of the transforms.
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Video 98. "The Biggest Ideas in the Universe | 15. Gauge Theory" by Sean Carroll (2020) Source. This attempts a one hour hand wave explanation of it. It is a noble attempt and gives some key ideas, but it falls a bit short of Ciro's desires (as would anything that fit into one hour?)
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Video 99. "The Symmetries of the universe" by ScienceClic English (2021) Source. https://youtu.be/hF_uHfSoOGA?t=144 explains intuitively why symmetry implies consevation!
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Ancestors

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