Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-08-31
J.Math.Phys.48:012303,2007
Physics
High Energy Physics
High Energy Physics - Theory
Approx. 14 pages. v2: minor corrections; conclusions unaffected
Scientific paper
10.1063/1.2408400
A formulation of the non-commutative geometry for the standard model of particle physics with a Lorentzian signature metric is presented. The elimination of the fermion doubling in the Lorentzian case is achieved by a modification of Connes' internal space geometry so that it has signature 6 (mod 8) rather than 0. The fermionic part of the Connes-Chamseddine spectral action can be formulated, and it is shown that it allows an extension with right-handed neutrinos and the correct mass terms for the see-saw mechanism of neutrino mass generation.
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