%0 Journal Article
%D 2014
%T Dirac operators on noncommutative principal circle bundles
%A Andrzej Sitarz
%A Alessandro Zucca
%A Ludwik Dabrowski
%X 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 → S2.
%I World Scientific Publishing
%G en
%U http://urania.sissa.it/xmlui/handle/1963/35125
%1 35363
%2 Mathematics
%4 1
%$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-02T15:58:16Z
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%R 10.1142/S0219887814500121
%0 Journal Article
%J Classical and Quantum Gravity. Volume 30, Issue 1, 7 January 2013, Article number 015006
%D 2013
%T Dirac operator on spinors and diffeomorphisms
%A Ludwik Dabrowski
%A Giacomo Dossena
%K gravity
%X 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.
%B Classical and Quantum Gravity. Volume 30, Issue 1, 7 January 2013, Article number 015006
%I IOP Publishing
%G en
%U http://hdl.handle.net/1963/7377
%1 7425
%2 Mathematics
%4 1
%# MAT/07 FISICA MATEMATICA
%$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-06-17T13:30:17Z
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%R 10.1088/0264-9381/30/1/015006
%0 Journal Article
%J Comm. Math. Phys. 295 (2010) 731-790
%D 2010
%T Dirac Operators on Quantum Projective Spaces
%A Francesco D'Andrea
%A Ludwik Dabrowski
%X 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