- #36
samalkhaiat
Science Advisor
- 1,802
- 1,200
Demystifier said:We already had this discussion, and I asked you a question that you never answered. I will ask you again. How ##\gamma^{\mu}## transforms under general coordinate transformations in curved spacetime? Until you answer that question, you will not convince me that you understand the things sufficiently well.
To be honest, I never answered because I came to the conclusion that you were talking about a subject you don’t fully understand. I also recall telling you that [itex]\gamma^{\mu}(x)[/itex], with [itex]\mu[/itex] being a world-index, is a short-hand notation, i.e., a definition which stands for [itex]e^{\mu}{}_{a}(x) \gamma^{a}[/itex]. The Diffeomorphism group as well as the local Lorentz group transform the veirbeins [itex]e^{\mu}{}_{a}(x)[/itex] and leave [itex]\gamma^{a}[/itex] invariant.