@article {2013,
title = {Dirac operator on spinors and diffeomorphisms},
journal = {Classical and Quantum Gravity. Volume 30, Issue 1, 7 January 2013, Article number 015006},
number = {arXiv:1209.2021v1;},
year = {2013},
note = {This article is composed of 13 pages and is recorded in PDF format},
publisher = {IOP Publishing},
abstract = {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.},
keywords = {gravity},
doi = {10.1088/0264-9381/30/1/015006},
url = {http://hdl.handle.net/1963/7377},
author = {Ludwik Dabrowski and Giacomo Dossena}
}
@mastersthesis {2012,
title = {Some aspects of spinors {\textendash} classical and noncommutative},
year = {2012},
school = {SISSA},
url = {http://hdl.handle.net/1963/6317},
author = {Giacomo Dossena}
}
@article {2011,
title = {Product of real spectral triples},
journal = {International Journal of Geometric Methods in Modern Physics 8 (2011) 1833-1848},
number = {arXiv:1011.4456;},
year = {2011},
note = {Based on the talk given at the conference \\\"Noncommutative Geometry and Quantum Physics, Vietri sul Mare, Aug 31 - Sept 5, 2009\\\"},
publisher = {World Scientific},
abstract = {We 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.},
doi = {10.1142/S021988781100597X},
url = {http://hdl.handle.net/1963/5510},
author = {Ludwik Dabrowski and Giacomo Dossena}
}