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Variational calculus is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find extrema of functionals: mappings from a set of functions to the real numbers. The archetype application in physics is Lagrangian mechanics, seeking extrema of action functionals.

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Tensor Question (Klein–Gordon equation) [closed]

I have a question following the derivation of the Klein-Gordon equation from a lagrangian. From Eq. (13d), where does $\delta^\mu_\nu$ come from? I guess it's a conversion factor of some sort.
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How to derive some part of the Proca lagrangian for a Vector (spin-1)? [closed]

I'm trying to derive Eq. (10.17) & Eq. (10.18) from the textbook. Where does the term -1/(4*pi) come from, and how do I cancel out the rest of the term (see my text, second picture).
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