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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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Is the path of stationary action unique? What are the physical implications of $L_{\dot{x}}=...

The Euler-Lagrange equations are obtained by employing the principle of least action. … This means that if we make a slight change to the path of the particle (call it $\delta x$(t)), the action should not change (to first order in $\delta x$). …
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3 votes
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Why is the value of the action integral in general relativity the same on all regions that a...

and then integrate over a Euclidean region when evaluating the action functional. … How does the action integral become a contour integral and why is it independent of the region? …
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