2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/189761A 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.Approx. 14 pages. v2: minor corrections; conclusions unaffectedHigh Energy Physics - TheoryOperator AlgebrasQuantum Algebratext