By definition a conformal transformation of the coordinates is an invertible mapping $x\rightarrow x'$ which leaves the metric invariant upto a scale factor: \begin{equation} g_{\mu\nu}'(x') = \Lambda(x) g_{\mu\nu}(x) \end{equation}

I am facing problems in deriving the scale factor for special conformal transformation (SCT). This transformation has the finite form given as: \begin{equation} {x'}^{\mu} = \frac{x^{\mu}-b^{\mu}x^2}{1-2(b.x)+b^2x^2} \end{equation} I was trying to derive the scale factor for this transformation using the metric condition: \begin{equation} g_{\mu\nu}'(x') =\frac{\partial x^\sigma}{\partial {x'}^\mu}\frac{\partial x^\rho}{\partial {x'}^\nu}g_{\sigma\rho}= \Lambda(x) g_{\mu\nu}(x) \end{equation} I was not able to find out $\Lambda(x)$, however the final form of scale factor $\Lambda(x)$ is given in the book as: \begin{equation} \Lambda(x) = (1-2b.x + b^2x^2)^2 \end{equation}


closed as off-topic by ACuriousMind, Kyle Kanos, joshphysics, Brandon Enright, Ali Sep 13 '14 at 18:01

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    $\begingroup$ And your question is? Plug the transformation in and look at the result! Please, also have a look at our homework policy and our stance on check-my-work questions. $\endgroup$ – ACuriousMind Sep 13 '14 at 14:37
  • $\begingroup$ Hello, welcome to SE. Could you try to clarify your question? What have you tried? Which point is causing trouble? I'm sure if you make it a little clearer, and say what you've tried, somebody might be able to help you. $\endgroup$ – innisfree Sep 13 '14 at 15:40