Kartik Prabhu
math/physics question (cc:@johncarlosbaez)
Take the group SL(2,C), the double cover of the identity-connected component of the Lorentz group. As a manifold this group is homeomorphic to R3 × S3, where R3 are Lorentz boosts and S3 the group SU(2) (double cover of rotations).
You can also view the R3 as a Riemannian hyperbolic space H3. Now H3 has a natural Lorentz invariant measure, and S3 has a natural rotation invariant measure. So the left-invariant Haar measure on SL(2,C) should be some positive function F times the measures on H3 and S3.
Is there an explicit expression for this Haar measure in term of some/any coordinates on H3 and S3?
(Asking here because I’m tired of the condescension on math/stack overflow towards explicit examples)