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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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Rules for calculating the energy-momentum tensor
In the expression $$\mathcal L_0=\frac{1}{2} g^{\alpha \beta} (\partial_\alpha \phi) (\partial_\beta \phi), $$ the indices $\alpha$ and $\beta$ are summation indices. On the other hand, in the formul …
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Derivation of Maxwell's equations using Lagrangian formalism
The use of the Lagrangian formalism is not restricted to (point) mechanics, but all fundamental interactions (electroweak, strong, gravitation) are defined by the action integral of a Lagrangian field …