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RE: The Euler-Lagrange Equation - Quantum Field Theory
See near 1 minute 20 seconds in this video for an example of what a Lagrangian density used by a field theorist looks like https://steemit.com/science/@nonlinearone/physics-out-loud-broken-symmetries-and-the-masses-of-gauge-bosons-by-peter-w-higgs-1964