In classical mechanics the Lagrangian is constructed as the difference between kinetic and potential energy, [tex]L=T-V,[/tex] and hence the physical interpretation is fairly straightforward when taken together with Hamiltons principle, i.e the system evolves "along the path of least resistance".(adsbygoogle = window.adsbygoogle || []).push({});

But now that I've started to study a little QFT I see that there the Lagrangian seems to be simply constructed as "the function that after applying Hamiltons principle gives the correct equation of motion". In other words, I don't see any obvious physical interpretation outside of being a lucky guess giving the correct result.

Have I missed something important here or is the Lagrangian just a mathematical tool and not something with a distinct physical interpretation like the Hamiltonian?

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# Interpretating the Lagrangian

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