Special Conformal Transformations

  • Thread starter Knecht
  • Start date
11
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Hello,

In conformal geometry there is a 15-parameter symmetry group.

I have an rough conceptual understanding of the 3 spatial translations, the 1 temporal translation, the 3 rotations, the 3 Lorentz "boosts", and the 1 dilation transformation.

I am having trouble conceptualizing the remaining 4 "special conformal transformations", which appear to be combinations of translations, rotations, and possibly something referred to as "inversion". Some have drawn a parallel to "accelerations"?

If there are any math aficionados out there who can give me a more intuitive, conceptual, visual understanding of what is going on physically with these special conformal transformations, I would be eternally grateful.

Maybe one approach might be to start with a homogeneous sphere and say: "Ok, when we subject the sphere to a SCT, these physical processes happen to the sphere.

Also, why are there specifically 4 SCTs?

Any help would be welcome and the more different perspectives, the better.

Yours in science
Knecht
www.amherst.edu/~rloldershaw
 

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