- #1

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## Main Question or Discussion Point

in varying an action like Polyakov's action with respect to the metric on the world sheet we have to consider the variation of the square root of the determinant. I have not found how to express the variation of the determinant of the metric. From reverse engineering I found that

[tex]\delta(h)=2 h h_{\alpha\beta}\delta(h^{\alpha\beta})[/tex]

can someone give a hint on how this is computed?

[tex]\delta(h)=2 h h_{\alpha\beta}\delta(h^{\alpha\beta})[/tex]

can someone give a hint on how this is computed?