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The action is the integral of the Lagrangian over time, or the integral of the Lagrangian Density over both time and space.

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What makes a Lagrangian a Lagrangian?

As far as I know there is no way of rigorously constructing a Lagrangian for a new physical theory. The point is you just have to guess a Lagrangian (i.e. construct your own theory), check all the inv …
Wojciech Morawiec's user avatar