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 - THES T1 - Some aspects of spinors – classical and noncommutative Y1 - 2012 A1 - Giacomo Dossena PB - SISSA UR - http://hdl.handle.net/1963/6317 U1 - 6218 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Product of real spectral triples JF - International Journal of Geometric Methods in Modern Physics 8 (2011) 1833-1848 Y1 - 2011 A1 - Ludwik Dabrowski A1 - Giacomo Dossena AB - 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. PB - World Scientific UR - http://hdl.handle.net/1963/5510 N1 - Based on the talk given at the conference \\\"Noncommutative Geometry and Quantum Physics, Vietri sul Mare, Aug 31 - Sept 5, 2009\\\" U1 - 5345 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER -