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My physics textbook asserts that the group of maps $f: M \rightarrow M $ ($M$ is the Minkowski space, i. e. $\Bbb R^4$ with the pseudonorm $||x||=x_0^2-x_1^2-x_2^2-x_3^2$ and scalar product $x\dot{} y=x_0y_0-x_1y_1-x_2y_2-x_3y_3$) with the property that for all events $p,q$ with $||p-q||=0$ we have $||f(p)-f(q)||=0$, is a 14 dimensional Lie group which is generated by the elements of the Poincaré group, the homotheties $x \mapsto \lambda x$ ($\lambda \in \Bbb R$) and the maps of the form $$x \mapsto \frac{x-a ||x||^2}{1-2a\dot{}x+||c||^2||x||^2}$$ with $a \in M$.

My questions are:

  • Are these statements true? (It's from a physics book, so you cannot know for sure.)

  • How do you prove them?

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1 Answer 1

up vote 1 down vote accepted

This is nicely done in the book of Martin Schottenloher, A Mathematical Introduction to Conformal Field Theory.

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