Abstract
It is shown that the non-commutative differential geometry fails to reproduce the most general Higgs potential of two-Higgs-doublets model. To recover physically sensible potential additional terms are needed. A general formula for inner products of basis two-forms in the non-commutative differential calculus is proposed by requiring that the inner products be expressed in terms of those of one-form basis. It leads to the absence of flavor changing neutral current in the tree level and of spontaneous jdP provided they are not induced by additional terms.
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