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 -