A conformal transformation is a coordinate transformation that leaves the metric invariant up to a scale change [itex]g_{\mu\nu}(x) \to g'_{\mu\mu}(x)=\Omega(x)g_{\mu\nu}(x)[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

This means that the length of vectors is not preserved: [itex]g_{\mu\nu}x'^{\mu}x'^{\nu}\not=g_{\mu\nu}x^{\mu}x^{\nu}[/itex]

But is [itex]g'_{\mu\nu}x'^{\mu}x'^{\nu}=g_{\mu\nu}x^{\mu} x^{\nu}[/itex] correct?

Best regards, physicus

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# Easy question on conformal transformations

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