I do not understand how people construct a suitable action which after variation will give the correct equation of motion. For example, the Einstein Hilbert action: S=integration[R d^4x] gives the equation of motion when varied with respect to [g_mu nu]. But no book I had read so far tells me how to construct this action. Can anybody help me with this?(adsbygoogle = window.adsbygoogle || []).push({});

Second, if someone says that the action is constructed so that after variation it must give the equation of motion then why do I need to use this technique in the first place where first I have to know the equation of motion and then construct the action, then vary it and rederive the equation of motion which I already had?

Third, how do I know that an action is the only action which will give the correct equation of motion?

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# How does one construct the action which gives the equation of motion?

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