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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 does "up to a total derivative" really mean and how should I know when to use it?
I am a mathematician who is taking a quantum field theory course without much prior pyhsics. We have had the term "up to a total derivative" a few times, yet every time I asked what it meant I didn't …