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How do spinors transform under diffeomorphisms?

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Indices of a usual vector bundle don't transform under spacetime diffeomorphisms. But it seems spinor indices are somehow intertwined with spacetime indices. I'm not familiar with spinors in GR and I'm at a loss here, please someone explain to me? Or give some references?

asked Jan 7, 2015 in Mathematics by xavier (85 points) [ revision history ]
edited Jan 9, 2015 by Jia Yiyang

The tetrad formalism is what you are looking for.

commented Jan 9, 2015 by Ron Maimon (7,730 points) [ no revision ]

Yes, the indices are intertwined and the "four-vector" linking tensors with spinors is the set of four sigma matrices (see e.g. Penrose, Rindler: Spinors and Space-time).

commented Mar 13, 2015 by Void (1,645 points) [ no revision ]

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