1,721,044 research outputs found
Group actions on spinors : lecture notes
No full textThese very sketchy and informal notes are based on lectures for physicists held at the SISSA, Trieste in 1985-1986 and at the INFN, Naples in 1986 (taken from the Preface of the book
A SUPERPOSITION PRINCIPLE FOR MIXED STATES
No full textAn approximate description of cyclic evolution of mixed states ρ (density matrices) is discussed in terms of vectors in R ⊗R (or Hilbert-Schmidt operators in R). It combines the decomposition ambiguity of ρ into pure states with the usual Berry phase for state vectors. The resulting non-Abelian quantum holonomy may be observable if the superposition principle is extended to R ⊗R © 1991 Società Italiana di Fisica
Towards a noncommutative Brouwer fixed-point theorem
No full textWe present some results and conjectures on a generalization to the noncommutative setup of the Brouwer fixed-point theorem from the Borsuk–Ulam theorem perspective. © 2016 Elsevier B.V
The Standard Model in noncommutative geometry and Morita equivalence
No full textWe discuss some properties of the spectral triple (AF,HF,DF,JF,γF) describing the internal space in the noncommutative geometry approach to the Standard Model, with AF=C⊕H⊕M3(C). We show that, if we want HF to be a Morita equivalence bimodule between AF and the associated Clifford algebra, two terms must be added to the Dirac operator; we then study its relation with the orientability condition for a spectral triple. We also illustrate what changes if one considers a spectral triple with a degenerate representation, based on the complex algebra BF=C⊕M2(C)⊕M3(C)
Real Spectral Triples on Crossed Products
Full text linkGiven a spectral triple on a unital -algebra and an equicontinuous
action of a discrete group on , a spectral triple on the reduced crossed
product -algebra was constructed by Hawkins, Skalski,
White and Zacharias in [On spectral triples on crossed products arising from
equicontinuous actions, Math. Scand. 113(2) (2013) 262-291], extending the
construction by Belissard, Marcolli and Reihani in [Dynamical systems on
spectral metric spaces, preprint (2010), arXiv:1008.4617], by using the
Kasparov product to make an ansatz for the Dirac operator. Supposing that the
triple on is equivariant for an action of , we show that the triple on
is equivariant for the dual coaction of . If moreover an
equivariant real structure is given for the triple on , we give
constructions for two inequivalent real structures on the triple .
We compute the KO-dimension with respect to each real structure in terms of the
KO-dimension of and show that the first and the second order conditions are
preserved. Lastly, we characterise an equivariant orientation cycle on the
triple on coming from an equivariant orientation cycle on the
triple on . We show, along the paper, that our constructions generalize the
respective constructions of the equivariant spectral triple on the
noncommutative -torus
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