New answers tagged action
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Where this definition $T_{\alpha\beta}=-\frac{2}{T}\frac{1}{\sqrt{-h}}\frac{\delta S}{\delta h^{\alpha \beta}}$ come from?
Because by construction, it satisfies 3 key properties one expects from the energy-momentum tensor:
It is a symmetric rank-2 tensor,
By an infinitesimal coordinate transformation $x^\mu\to x^\mu+\xi^\...
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Identifying Lagrangian as the solution to the variational problem from the Hamilton's principle
If there is a d'Alembert's principle, then we can show Lagrange equations, cf. e.g. this Phys.SE post. If Lagrange equations are of the form of Euler-Lagrange equations, then the corresponding action ...
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Identifying Lagrangian as the solution to the variational problem from the Hamilton's principle
In a general problem involving an integral of the form
$$I=\int_{x_1}^{x_2}f(x,y(x),y'(x)) \ dx $$
we know that we can obtain the generic Euler-Lagrange equations. The "identification" is ...
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