TY - JOUR
T1 - Dirac operator on spinors and diffeomorphisms
JF - Classical and Quantum Gravity. Volume 30, Issue 1, 7 January 2013, Article number 015006
Y1 - 2013
A1 - Ludwik Dabrowski
A1 - Giacomo Dossena
KW - gravity
AB - 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.
PB - IOP Publishing
UR - http://hdl.handle.net/1963/7377
N1 - This article is composed of 13 pages and is recorded in PDF format
U1 - 7425
U2 - Mathematics
U4 - 1
U5 - MAT/07 FISICA MATEMATICA
ER -