Let’s derive the Lagrangian for the photon field (the electromagnetic field).

in the end, want to clarify the math symbols:

Fμν​ (Fμν​=∂μ​Aν​−∂ν​Aμ​) is simply the components of the 2-form F=dAF = dAF=dA:$$F = dA = \frac12 F_{\mu\nu} dx^\mu \wedge dx^\nu$$F=dA=21​Fμν​dxμ∧dxν