Uploaded January 2019 | Updated September 2026, 18 hours ago
In this video, I show you how to derive the Maxwell Lagrangian density starting with Maxwell's equations in integral form.
My Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
Superfluid Helium Resonance Experiment video:
youtu.be/unUNQNmuvUQ
A worthwhile clarification about the gauge invariance of electromagnetism is given in this physics.stack exchange post:
physics.stackexchange.com/a/353848/47309
Basically, it points out that the gauge group is only specifically U(1) once we couple it to the Dirac field (at least in the context of the later videos in this series). For free E & M, it could be U(1) or R. There is no way to tell until we couple it to other fields (all we know is that the algebra is u(1) ), at which point we select U(1) because that is the original global symmetry of the Dirac lagrangian. I should have noted this in the video, but didn't think of it. A commenter pointed it out.
In this video, I show you how to derive the Maxwell Lagrangian density starting with Maxwell's equations in integral form.
My Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
Superfluid Helium Resonance Experiment video:
youtu.be/unUNQNmuvUQ
A worthwhile clarification about the gauge invariance of electromagnetism is given in this physics.stack exchange post:
physics.stackexchange.com/a/353848/47309
Basically, it points out that the gauge group is only specifically U(1) once we couple it to the Dirac field (at least in the context of the later videos in this series). For free E & M, it could be U(1) or R. There is no way to tell until we couple it to other fields (all we know is that the algebra is u(1) ), at which point we select U(1) because that is the original global symmetry of the Dirac lagrangian. I should have noted this in the video, but didn't think of it. A commenter pointed it out.
