%0 Journal Article
%J Classical and Quantum Gravity. Volume 30, Issue 1, 7 January 2013, Article number 015006
%D 2013
%T Dirac operator on spinors and diffeomorphisms
%A Ludwik Dabrowski
%A Giacomo Dossena
%K gravity
%X 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 $S_{\sigma, g}$ of spinor fields on $M$ and a Hilbert space $\HH_{\sigma, g}= L^2(S_{\sigma, g},\vol{M}{g})$ of $L^2$-spinors of $S_{\sigma, g}$. 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 $f\in \diff{M}$ lifts in exactly two ways to a unitary operator $U$ from $\HH_{\sigma, g} $ to $\HH_{f^*\sigma,f^*g}$. 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.
%B Classical and Quantum Gravity. Volume 30, Issue 1, 7 January 2013, Article number 015006
%I IOP Publishing
%G en
%U http://hdl.handle.net/1963/7377
%1 7425
%2 Mathematics
%4 1
%# MAT/07 FISICA MATEMATICA
%$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-06-17T13:30:17Z
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%R 10.1088/0264-9381/30/1/015006