A Field-Theoretic Approach to Connes' Gauge Theory on $M_4\times Z_2$

Details A Field-Theoretic Approach to Connes' Gauge Theory on $M_4\times Z_2$ A Field-Theoretic Approach to Connes' Gauge Theory on $M_4\times Z_2$

2000-10-27

arxiv.org/abs/hep-th/0010253v1

Int.J.Mod.Phys. A16 (2001) 3203-3216

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX file, 16 pages

Scientific paper

10.1142/S0217751X01004876

Connes' gauge theory on $M_4\times Z_2$ is reformulated in the Lagrangian level. It is pointed out that the field strength in Connes' gauge theory is not unique. We explicitly construct a field strength different from Connes' one and prove that our definition leads to the generation-number independent Higgs potential. It is also shown that the nonuniqueness is related to the assumption that two different extensions of the differential geometry are possible when the extra one-form basis $\chi$ is introduced to define the differential geometry on $M_4\times Z_2$. Our reformulation is applied to the standard model based on Connes' color-flavor algebra. A connection between the unimodularity condition and the electric charge quantization is then discussed in the presence or absence of $\nu_R$.

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