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A solution of the so-called fermion doubling problem in Connes'Noncommutative Standard Model has been given by Barrett in 2006 in the form ofMajorana-Weyl conditions on the fermionic field. These conditions define a${\cal U}_{J,\chi}$-invariant subspace of the correct physical dimension, where${\cal U}_{J,\chi}$ is the group of Krein unitaries commuting with thechirality and real structure. They require the KO-dimension of the total tripleto be $0$. In this paper we show that this solution is, up to some trivialmodifications, and under some mild assumptions on the finite triple, the onlyone with this invariance property. We also observe that a simple modificationof the fermionic action can act as a substitute for the explicit projection onthe physical subspace.

On the uniqueness of Barrett's solution to the fermion doubling problem in Noncommutative Geometry