# 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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### Varying $\Box h_{\lambda\kappa} \Box h^{\lambda\kappa}$ with respect to $h_{\mu \nu}$ [closed]

I'm trying to gain a working understanding of the basic calculus of variations used in field theories, and I'm a little stuck trying to understand a step I've seen in a derivation. I'm sure my ...
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### Deriving the Noether's theorem

I am familiar with how Noether's theorem is derived in some sources/books, the answer in 534699 is particularly clear. However, I'm reading A First Book of Quantum Field Theory by Pal, and although ...
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### Changing coordinate system [migrated]

Someone please explain how did we get second term in equation 2.15.
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### Variation of the derivative of field in 2d Sigma model

Consider 2d Sigma model, the Lagrangian is: $$\mathcal{L} = \frac{1}{2}\eta_{\mu\nu}\partial_{\alpha}X^{\mu}\partial_{\beta}X^{\nu}\sqrt{-h}h^{\alpha\beta}$$ where $\eta=(-,+,+,\dots)$ is $D$-...