I remember when I learnt some basic continuum mechanics, Lagrangian is just a integral of lagrangian density over space, which is quite easy to accept because it's just a continuous version of L=T-U. Now I'm trying to start a bit QFT and notice that Lagrangian is an integral over space-time, and I just can't quite accept the integral over time part.(adsbygoogle = window.adsbygoogle || []).push({});

I suppose in classical relativistic field theory one must include the integral over time to get the correct equation of motion, but I can't find any introductory article about this on the net, so could you guys provide some guidance? I just want to convince myself that we need the integral over time.

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# Why in field theory Lagrangian is an integral of space-time

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