For every continuous symmetry in the system (Lie group), there is a corresponding conservation law.

Furthermore, given the symmetry, we can calculate the derived conservation law, and vice versa.

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-Euclidean geometry, e.g. the pendulum lives on an infinite cylinder.

- Lagrangian mechanics | 907, 2k, 19
- Mechanics | 14, 2k, 51
- Physics | 276, 46k, 825
- Natural science | 0, 61k, 2k
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- Ciro Santilli's Homepage | 262, 218k, 4k

- Lie group | 278, 5k, 72
- Local symmetries of the Lagrangian imply conserved currents | 168
- Lecture 3 | 171
- Why do symmetries such as SU(3), SU(2) and U(1) matter in particle physics? | 543
- Yang-Mills existence and mass gap | 374, 374, 1