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/1963/737700324nas a2200097 4500008004100000245006100041210005700102260001000159100002100169856003600190 2012 en d00aSome aspects of spinors – classical and noncommutative0 aSome aspects of spinors classical and noncommutative bSISSA1 aDossena, Giacomo uhttp://hdl.handle.net/1963/631700741nas a2200121 4500008004100000245003700041210003700078260002100115520040400136100002200540700002100562856003600583 2011 en d00aProduct of real spectral triples0 aProduct of real spectral triples bWorld Scientific3 aWe construct the product of real spectral triples of arbitrary finite dimension (and arbitrary parity) taking into account the fact that in the even case there are two possible real structures, in the odd case there are two inequivalent representations of the gamma matrices (Clifford algebra), and in the even-even case there are two natural candidates for the Dirac operator of the product triple.1 aDabrowski, Ludwik1 aDossena, Giacomo uhttp://hdl.handle.net/1963/5510