Q&A on String Theory Course Indices/QFT

In summary, the Spinor index is used when dealing with matrix elements of the operators of a spinor group (SL(2,C)). The Spinor index is attached to the spinor itself, not the Dirac spinor.
  • #36
latentcorpse said:
so to summarise, the transformation in Minkowski space (the first one i wrote down) had latin indices because in Minkowski space we can define spinor transformations and this will hold in any basis so we can move to abstract indices.

However, in a curved spacetime we cannot define spinor transformations so we need to move to flat spacetime (where we use greek indices) and the objects we use in the second transformation I wrote down will be related to their corresponding curved space quantities using veirbeins?

Roughly correct. As far as the curved-space quantities, I can't see any reason why you would learn anything from transforming the local Lorentz transformation matrix into curved indices.
 
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  • #37
This is beyond me...
 
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