- #1
maverick280857
- 1,789
- 4
Hi,
I am working through Chapter 4 of Francesco, Mathieu and Senechal's CFT book (https://www.amazon.com/dp/038794785X/?tag=pfamazon01-20). 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!
I am working through Chapter 4 of Francesco, Mathieu and Senechal's CFT book (https://www.amazon.com/dp/038794785X/?tag=pfamazon01-20). 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!