From Dirac to Langrangian

If you follow textbook, you would have learned Lagrangian then Dirac Equation, but in real history, it was other way around.

Paul Dirac Combine quantum mechanics with special relativity and Fix problems with the Klein–Gordon equation:

Only afterward did physicists realized that this equation can come from a Lagrangian and proved it.

Another interesting thing is confusion between curvature of space and particle involvement in origin of force. Again, the textbook just dump these two ABSTRCT narratives/conclusions to the students without providing the real history and connection between the two, making physics daunting.

The question we should ask is what’s the essence of force? It bothered Newton in his lifetime, because it’s such a hard problem!

Today we know Forces are just interactions mediated by field quanta, we can discover it via momentum exchange, i.e. Lagrangian Equation in QFT.

Without a particle carrying charge/current, the photon field cannot generate a classical force, and there are not only electric current leading to electromagnetism force, but also weak current leading to weak force, and color current leading to strong focce!

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