In this video we talk about Maxwell's equations written in terms of potentials (scalars and vectors) and we approach a central concept in theoretical physics: gauge invariance. The session was divided into two videos, the rest is available here: • Introduction to gauge theories (s... This video follows this one on Maxwell's equations, • Electromagnetism and Theoretical Physics ------------------------------------------------------------------- My name is Antoine Bourget, I am a theoretical physicist, and I try to convey in video what I find elegant in mathematics and physics. To follow the news of the channel, and contact me, you can join the Discord server or follow me on social networks. If you want to make a donation, I also have a Tipeee Discord account: / discord Twitter: / antoinebrgt My personal website: http://www.antoinebourget.org Tipeee: https://fr.tipeee.com/scientia-egregia/ ------------------------------------------------------------------- Plan 00:00 Start of the chat 5:33 Start of the video Part 1: reminders of previous episodes 10:30 Maxwell's equations 17:00 Reformulation in terms of forms 22:33 Relativistic formulation Part 2: Potentials 25:25 Idea of ​​potentials 27:00 Poincaré's lemma 34:20 Return to the E and B fields, scalar and vector potentials 40:30 Coupled equations satisfied by potentials Part 3: Gauge 50:50 Ambiguity on potentials 54:10 Principle of gauge invariance 1:04:00 Application to the decoupling of equations Conclusion (preview of the next video) 1:11:00 Principal bundles 1:15:00 Yang-Mills, weak and strong interactions References: - Bjorn Felsager, Geometry, Particles and Fields - Theodore Frankel, The geometry of physics - Mikio Nakahara, Geometry, Topology and Physics - M. Daniel and CM Viallet, The geometrical setting of gauge theories of the Yang-Mills type (accessible at http://www.lpthe.jussieu.fr/~viallet/...)