01202nas a2200133 4500008004100000245005000041210005000091260001900141520081700160653001200977100002200989700002101011856003601032 2013 en d00aDirac operator on spinors and diffeomorphisms0 aDirac operator on spinors and diffeomorphisms bIOP Publishing3 aThe 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.10agravity1 aDabrowski, Ludwik1 aDossena, Giacomo uhttp://hdl.handle.net/1963/7377