TY - JOUR
T1 - Dirac operators on noncommutative principal circle bundles
Y1 - 2014
A1 - Andrzej Sitarz
A1 - Alessandro Zucca
A1 - Ludwik Dabrowski
AB - 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.
PB - World Scientific Publishing
UR - http://urania.sissa.it/xmlui/handle/1963/35125
U1 - 35363
U2 - Mathematics
U4 - 1
ER -
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 -
TY - JOUR
T1 - Dirac Operators on Quantum Projective Spaces
JF - Comm. Math. Phys. 295 (2010) 731-790
Y1 - 2010
A1 - Francesco D'Andrea
A1 - Ludwik Dabrowski
AB - 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