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Change of determinant of metric

  1. Jun 21, 2014 #1


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    Under a change of variables:
    [itex]x^{\mu} \rightarrow x^{\mu}+ \delta x^{\mu}[/itex]

    How can I see how the determinant of the metric changes?
    [itex] \sqrt{|g(x)|}[/itex]?

    Is it correct to see it as a function?
    [itex] f(x) \rightarrow f(x+ \delta x) = f(x) + \delta x^{\mu} \partial_{\mu} f(x) [/itex]
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  3. Jun 21, 2014 #2


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