A field-theoretic approach to Connes' gauge theory on M-4 x Z(2)

Connes' gauge theory on M-4 x Z(2) is reformulated in the Lagrangian level. It is pointed out that the field strength in Connes' gauge theory is not u nique. We explicitly construct a field strength different from Connes' and prove that our definition leads to the generation-number independent Higgs potential. It is also shown that the nonuniqueness is related to the assump tion that two different extensions of the differential geometry are possibl e when the extra one-form basis x is introduced to define the differential geometry on M4 x Z2. Our reformulation is applied to the standard model bas ed on Connes' color-flavor algebra. A connection between the unimodularity condition and the electric charge quantization is then discussed in the pre sence or absence of nu (R).