The standard model in noncommutative geometry and fermion doubling

The link between chirality in the fermion sector and (anti-)self-duality in the boson sector is reexamined in the light of Connesʹ noncommutative geometry approach to the Standard Model. We find it to impose that the noncommutative Yang–Mills action be symmetrized in an analogous way to the Dirac–Yukawa operator itself.