@article {2014,
title = {Dirac operators on noncommutative principal circle bundles},
number = {International Journal of Geometric Methods in Modern Physics;volume 11; issue 1; article number 1450012;},
year = {2014},
publisher = {World Scientific Publishing},
abstract = {We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle. Examples of low-dimensional noncommutative tori are analyzed in more detail and all connections found that are compatible with an admissible Dirac operator. Conversely, a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection is exhibited. These examples are extended to the theta-deformed principal U(1)-bundle S 3 θ {\textrightarrow} S2.},
doi = {10.1142/S0219887814500121},
url = {http://urania.sissa.it/xmlui/handle/1963/35125},
author = {Andrzej Sitarz and Alessandro Zucca and Ludwik Dabrowski}
}
@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}
}
@article {2010,
title = {Dirac Operators on Quantum Projective Spaces},
journal = {Comm. Math. Phys. 295 (2010) 731-790},
number = {SISSA;17/2009/FM},
year = {2010},
note = {Quantum Algebra},
abstract = {We construct a family of self-adjoint operators D_N which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CP_q(l), for any l>1 and 0