407 research outputs found
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
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
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)
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