- www.youtube.com/watch?v=nrBiDRZRK5g Maxwell Lagrangian Derivation by Dietterich Labs (2019)
- www.youtube.com/watch?v=yo-Z3RO-eeY Deriving the Maxwell Lagrangian by Pretty Much Physics (2019)
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The source-free electromagnetic Lagrangian density is quadratic in the electromagnetic field tensor. Its Euler-Lagrange field equation is . Antisymmetry of makes the density invariant under gauge transformations, and contraction of its indices makes it a Lorentz scalar.