TODO. I think this is the key point. Notably, $U(1)$ symmetry implies charge conservation.

More precisely, each generator of the corresponding Lie algebra leads to one separate conserved current, such that a single symmetry can lead to multiple conserved currents.

This is basically the local symmetry version of Noether's theorem.

Then to maintain charge conservation, we have to maintain local symmetry, which in turn means we have to add a gauge field as shown at Video 93. "Deriving the QED Lagrangian by Dietterich Labs (2018)".

Forces can then be seen as kind of a side effect of this.

- Local symmetry | 162, 300, 1
- Continuous symmetry | 18, 318, 2
- Lie group | 233, 2k, 24
- Differential geometry | 12, 2k, 25
- Geometry | 0, 2k, 34
- Mathematics | 17, 13k, 336
- Ciro Santilli's Homepage | 262, 182k, 3k

- Derivation of the quantum electrodynamics Lagrangian | 269
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- Lie group | 233, 2k, 24
- What does it mean that photons are force carriers for electromagnetism? | 385
- Yang-Mills existence and mass gap | 374, 374, 1