Abstract
We discuss the action of diffeomorphisms on spinors on an oriented manifoldM. To do this, we first describe the action of the diffeomorphism groupD(M) on the set Π =H 1 (M,Z 2) of inequivalent spin structures and show that it is affine. We argue that in the presence of spinors the gauge group of gravity is a certain double cover ofD(M) which depends on the spin structure. We explicitly compute the action ofD(M) on Π whenM is a closed Riemann surface; Π is seen to consist of exactly two orbits, corresponding to even and odd spin structures.
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Communicated by S.-T. Yau
On leave of absence from I.F.T., University of Wrocław, Poland
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Dąbrowski, L., Percacci, R. Spinors and diffeomorphisms. Commun.Math. Phys. 106, 691–704 (1986). https://doi.org/10.1007/BF01463403
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DOI: https://doi.org/10.1007/BF01463403