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I am working through Chapter 4 of Francesco, Mathieu and Senechal's CFT book (https://www.amazon.com/Conformal-Theory-Graduate-Contemporary-Physics/dp/038794785X). Equation 4.52 states that for a special conformal transformation

[tex]\left|\frac{\partial\textbf{x'}}{\partial\textbf{x}}\right| = \frac{1}{(1-2(\textbf{b}\cdot\textbf{x})+b^2 x^2)^{d}}[/tex]

where |.| denotes the determinant. I know that

[tex]x'^{\mu} = \frac{x^\mu - b^\mu x^2}{1-2 b\cdot x + b^2 x^2}[/tex]

How does this give the determinant above? I would appreciate a hint.

Thanks in advance!

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# Determinant of a special conformal transformation

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