Models of Electroweak Interactions in Non-commutative Geometry: a Comparison

Alain Connes’ construction of the standard model is based on a generalized Dirac-Yukawa operator and the K-cycle (H,D), with H a fermionic Hilbert space. If this construction is reformulated at the level of the differential algebra then a direct comparison with the alternative approach by the Marseille-Mainz group becomes possible. We do this for the case of the toy model based on the structure group U(1)×U(1) and for the SU(2)×U(1) of electroweak interactions. Connes’ results are recovered without the somewhat disturbing γ5-factors in the fermion mass terms and Yukawa couplings. We discuss both constructions in the same framework and, in particular, pinpoint the origin of the difference in the Higgs potential obtained by them. ∗) Work supported in part by PROCOPE project Mainz University and CPT MarseilleLuminy 1 Also at CERN, CH-1211 Geneva 23