QED Prerequisites: The basics of gauge transformations

In this lesson we study the basic ideas behind gauge transformation in classical electromagnetic theory. We convert Maxwell's equations into their potential-based form and then discuss why we can "choose a gauge" to simplify the resulting equations. We introduce the elementary ontology used by most physicists regarding the interpretation of the "reality" of gauge fields versus the reality of the electromagnetic field.
Please consider supporting this channel on Patreon: / xylyxylyx
The software I usually use to produce the lectures is:
apps.apple.com/us/app/vittle-...

[@TrailersReheard]

Great lecture as always!

[@XylyXylyX]

Glad you think so!

[@mastershooter64]

Hello! When will you continue the mathematical foundations of quantum mechanics series? also thank you for all your videos they help me a lot! especially the tensors and manifold playlists right now

[@XylyXylyX]

Not sure yet. It wasn't very popular and the material is very difficult.

[@mattstarbuck7484]

love the video! I was just wondering whether there is meant to be a 1/c^2 in front of the A double dot at 14:23? Thank you :)

[@XylyXylyX]

Yep. That factor should be distributed with the time derivative.

[@giampierochiavarotti4107]

Great lecture...please add sutitles captions.. thank

[@TrailersReheard]

I think next lecture, if its not already planned, it would be worthwhile to mention 'residual' gauge invariance. I.e. even after choosing say, the Lorenz gauge, you can still of course shift by some function G such that □G=0. And you remain in a different Gauge which is still a Lorenz gauge

[@XylyXylyX]

Didn’t I mention that in this video? That is a good point.

[@TrailersReheard]

@@XylyXylyX don't recall, could have been implied/mentioned and I missed it!

[@theorist_1]

Hi there, would you like to assign proper serial no. to your videos.

[@sahhaf1234]

Yess, I second that request...

[@XylyXylyX]

This is a bit harder than it sounds given the freestyle way I produce the material. However, the order the material lies in the playlist is the order of intended viewing.

[@hafizajiaziz8773]

21:33 What's the F? 😀

[@khaledhasan8495]

Some scalar function that you have the luxury to choose

[@KipIngram]

7:54 - But... that's WRONG. A has direct physical effects in the world; Aharonov and Bohm demonstrated this in 1959. The potentials are real. So I guess you can "adopt" any position you want, but you should at least tell people that those fields have real demonstrable physical effects.