Dirac operator on spinors and diffeomorphisms

作者：Dabrowski Ludwik^*; Dossena Giacomo

来源：Classical and Quantum Gravity, 2013, 30(1): 015006.

DOI：10.1088/0264-9381/30/1/015006

The issue of general covariance of spinors and related objects is reconsidered. Given an oriented manifold M, to each spin structure sigma and Riemannian metric g there is associated a space S-sigma,S-g of spinor fields on M and a Hilbert space H-sigma,H-g = L-2(S-sigma,S-g, vol(g)(M)) of L-2-spinors of S-sigma,S-g. The group Diff(+)(M) of orientation-preserving diffeomorphisms of M acts both on g (by pullback) and on [sigma] (by a suitably defined pullback f*sigma). Any f is an element of Diff(+)(M) lifts in exactly two ways to a unitary operator U from H-sigma,H-g to H-f*sigma,H-,H-f*g. The canonically defined Dirac operator is shown to be equivariant with respect to the action of U, so in particular its spectrum is invariant under the diffeomorphisms.

• 出版日期2013-1-7