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How to raise and lower indices of gamma matrix in curved spacetime? Do we raise and lower the index of gamma matrix with $ g_{\mu \nu} $?

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Gamma matrices with flat (curved) indices are raised & lowered with the flat (curved) metric, respectively.

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  • $\begingroup$ Bigger question would be how to construct gamma matrices with curved indices.... $\endgroup$ – lalala Jul 3 '18 at 8:24
  • $\begingroup$ Yes. One should then multiply with the vielbein (or its inverse). $\endgroup$ – Qmechanic Jul 3 '18 at 8:55

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