3

By preserving angles obviously, har.. har...

In all seriousness, I can appreciate the Lorentz group for 4D being written $O(1,3)$ the same way we write our spacetime $\mathbb{R}^{1,3}$. The Lorentz group is turned inside out in all undergraduate curriculums.

I get that in $O(2,4)$ the extra "temporal" part arises from out dilations and special conformal transformations but it remains very abstract to me and I haven't been able to find any source that goes through the process so that it is no longer something I just accept that has been derived and move on. I came upon the topic when looking at the compactification of $\mathbb{R}^{1,1}$

Appreciate any help!

Qmechanic
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Deniz Gün
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1 Answers1

1

For what it's worth, the main point is that the conformal compactification $\overline{\mathbb{R}^{p,q}}$ of $\mathbb{R}^{p,q}$ naturally sits inside $\mathbb{R}^{p+1,q+1}$, cf. e.g. this Phys.SE post and Ref. 1.

References:

  1. M. Schottenloher, Math Intro to CFT, Lecture Notes in Physics 759, 2008; Chapter 1 & 2.
Qmechanic
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