- #1
Rocky Raccoon
- 36
- 0
While it's pretty easy to derive the infinitesimal version of the special conformal transformation of the coordinates:
[tex]x'^{\mu}=x^{\mu}+c_{\nu}(x^{\mu} x^{\nu}-g^{\mu \nu} x^2)[/tex]
with c infinitesimal,
how does one integrate it to obtain the finite version transformation:
[tex]x'^{\mu}=\frac{x^{\mu}-x^2 c^{\mu}}{1-2 x^{\nu} c_{\nu} + x^2 c^2}[/tex]
with c finite?
I've never delt with nonlinear transformations that don't exponentiate trivially. Also, how does one integrate over a parameter that is Lorentz contracted with another vector?
Thanks for your help.
[tex]x'^{\mu}=x^{\mu}+c_{\nu}(x^{\mu} x^{\nu}-g^{\mu \nu} x^2)[/tex]
with c infinitesimal,
how does one integrate it to obtain the finite version transformation:
[tex]x'^{\mu}=\frac{x^{\mu}-x^2 c^{\mu}}{1-2 x^{\nu} c_{\nu} + x^2 c^2}[/tex]
with c finite?
I've never delt with nonlinear transformations that don't exponentiate trivially. Also, how does one integrate over a parameter that is Lorentz contracted with another vector?
Thanks for your help.