Open AccessNoncommutative geometry and reality
Author(s) -
Alain Connes
Publication year - 1995
Publication title -
journal of mathematical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.708
H-Index - 119
eISSN - 1089-7658
pISSN - 0022-2488
DOI - 10.1063/1.531241
Subject(s) - noncommutative geometry , mathematics , spectral triple , spectral geometry , duality (order theory) , pure mathematics , poincaré duality , geometry , algebra over a field , noncommutative quantum field theory , cohomology
We introduce the notion of real structure in our spectral geometry. This notion is motivated by Atiyah’s KR‐theory and by Tomita’s involution J. It allows us to remove two unpleasant features of the ‘‘Connes–Lott’’ description of the standard model, namely, the use of bivector potentials and the asymmetry in the Poincare duality and in the unimodularity condition.
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