Uploaded December 2018 | Updated September 2026, 3 hours ago
In this video, I show you how to derive the Lagrangian density of quantum electrodynamics, which is one of the most successful physical theories ever purposed.
My Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
Maxwell Lagrangian Derivation Video: youtube.com/watch?v=nrBiDRZRK5g
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 our context). 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 Lagrangian density of quantum electrodynamics, which is one of the most successful physical theories ever purposed.
My Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
Maxwell Lagrangian Derivation Video: youtube.com/watch?v=nrBiDRZRK5g
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 our context). 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.
