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Questions tagged [variational-calculus]

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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Energy-momentum Tensor for a Real Scalar Field Lagrangian

I'm currently working through Schwartz's QFT book, and I'm trying to find the energy-momentum tensor for the following Lagrangian: $$L = -\frac{1}2\phi(\Box+m^2)\phi.$$ Am I correct in thinking ...
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Lagrangian non-relativistic limit to the non-relativistic action: lagrangian of a free particle

Let be $u=|\bar{u}|$ the speed of a free particle (at constant speed) of mass $m$ that is moving in relation to an inertial frame. Why we initially introduce the term $\epsilon$ to the free lagrangian ...
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How to go from $\delta(\dot{\Psi})$ to $\delta\Psi$ in variational calculations? [duplicate]

This must have been done somewhere before but I never saw a clear and rigorous explanation of why. This is possibly related to my recent post here about potential abuse of notation. Just to be ...