It is known as a fact that conformal maps on Rn→Rn for n>2 are rotations, dilations, translations, and special transformations while conformal maps for n=2 are from a much wider class of maps, holomorphic/antiholomorphic maps. I was wondering to know if there is any topological or geometrical description for this.
To show what I mean, consider this example: in Rn for n>2 interchanging particles can only change the wave function to itself or its minus. It is related to the fundamental group of Rn−x0 (x0 is a point in Rn and π1(Rn−{x0})=e for n>2) but this is not true for n=2.
I want to know whether exists any topological invariant or just any geometrical explanation that is related to the fact that I mentioned about conformal maps on Rn.
No comments:
Post a Comment