%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 Thesis
%D 2012
%T Some aspects of spinors – classical and noncommutative
%A Giacomo Dossena
%I SISSA
%G en
%U http://hdl.handle.net/1963/6317
%1 6218
%2 Mathematics
%3 Mathematical Physics
%4 -1
%$ Submitted by Giacomo Dossena (dossena@sissa.it) on 2012-11-13T11:13:08Z\\nNo. of bitstreams: 1\\nthesis.pdf: 1569621 bytes, checksum: 1ab89dce9cdc2097b3692da5a63ad82b (MD5)
%0 Journal Article
%J International Journal of Geometric Methods in Modern Physics 8 (2011) 1833-1848
%D 2011
%T Product of real spectral triples
%A Ludwik Dabrowski
%A Giacomo Dossena
%X 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.
%B International Journal of Geometric Methods in Modern Physics 8 (2011) 1833-1848
%I World Scientific
%G en
%U http://hdl.handle.net/1963/5510
%1 5345
%2 Mathematics
%3 Mathematical Physics
%4 -1
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-02-16T16:08:08Z\\nNo. of bitstreams: 1\\n1011.4456v1.pdf: 279 bytes, checksum: 44d0388a861dfb41e598ee6d79dc9d01 (MD5)
%R 10.1142/S021988781100597X