What is the meaning of the 0 in the Special Orthogonal group index? Here is an example: $SO_{0}(3)$ or $SO_{0}(3,1)$. I think (3,1) stands for the Lorentzian metric, right? I found this notation on http://math.ucr.edu/home/baez/gravitational.html.
2026-03-31 09:40:02.1774950002
What is the meaning of the 0 in the Special Orthogonal group index?
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The full Lorentz group $SO(3,1)$ (as a Lie group) is not connected. $SO_0(3,1)$ is that part of the group that is connected to the identity. So it's a subgroup. The disconnected part contains things like time-reversal, which is often physically irrelevant because you can't do an "infinitesimal generator" of that. (in mathematical language you could say that $SO$ and $SO_0$ have the same Lie-algebra, which captures the concept of infinitesimal symmetry).