- #1
physicus
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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].
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?
physicus
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?
physicus