In my ST book the world sheet EM tensor for the Polyakov action is given by(adsbygoogle = window.adsbygoogle || []).push({});

[tex]T_{\alpha \beta} = -\frac{2}{T} \frac{1}{\sqrt{-h}} \frac{\delta S_{\sigma}}{\delta h^{\alpha \beta}}[/tex]

Why is this?

(Searching through the internet I found clues to what is called Hilbert's prescription, namely that the EM tensor in GR is given by

[tex]T^{\mu \nu} = -2 \frac{\delta L}{\delta g^{\mu \nu}}[/tex]

and that to obtain the conserved current one should calculate the functional derivative of the Lagrangian L wrt the gauge field. Why is this all so?!)

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# World sheet EM tensor (Hilbert principle?)

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