Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
up vote 1 down vote accepted

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

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.