Hey people, I am currently studying theoretical particle physics but had to do a bit of reading on general relativity, which I barely know anything about, for some exercises we were given. I read that Carroll's "spacetime and geometry" was a very good book so I used that. I've hit on a weird notation in the book for writing Jacobians. Carroll uses the same index in the nominator as in the denominator (see picture) and he consistently does this, so it can't have been a typo. If he implies Einstein sum convention, this would give the trace of the Lorentz matrix under a Poincaré trafo on flat spacetime which is not 1 in general! If he doesn't imply sum convention it would be even weirder because the left hand side doesn't have a Lorentz index. Now, I didn't read the book beginning to end so it's possible that I have missed an explanation for this at an earlier point.…