- #1
S. Leger
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Homework Statement
I'm trying to calculate the variation of the following term for the determinant of the metric in the polyakov action:
$$h = det(h_{ab}) = \frac{1}{3!}\epsilon^{abc}\epsilon^{xyz}h_{ax}h_{by}h_{cz}$$
I know that there are some other ways to derive the variation of a metric, e.g. with the help of Jacobi's formula. But what I mean is the "trick" to derive it from exactly this term above.
Can someone show me?
How can I translate the result into factors of $h_{ab}$ and $h$?
Homework Equations
The Attempt at a Solution
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