While it's pretty easy to derive the infinitesimal version of the special conformal transformation of the coordinates:(adsbygoogle = window.adsbygoogle || []).push({});

[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.

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# Integrating infinitesimal conformal transformations

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