Standard Model in Differential Geometry on Discrete Space M_4 × Z_3 : Particles and Fields

概要

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Standard model is reconstructed using the generalized differential calculus extended on the discrete space M_4 × Z_3. Z_3 is necessary for the inclusion of strong interaction. Our starting point is the generalized gauge field expressed as A(x,y)=Σ_ia_i(x,y)da_i(x,y), (y =0,±), where a_i(x,y) is the square matrix valued function defined on M_4 × Z_3 and d=d+d_x is generalized exterior derivative. We can construct the consistent algebra of d_x with the introduction of the symmetry breaking function M(y) and the spontaneous breakdown of gauge symmetry is coded in d_x. The gauge field A_μ(x, y) and Higgs field Φ(x, y) are written in terms of a_i(x, y) and M(y),which might suggest a_i(x, y)to be more fundamental object.The unified picture of the gauge field and Higgs field as the generalized connection in noncommutative geometry is realized. Two model constructions are presented,which are distinguished in the particle assignment of Higgs field Φ(x, y). Within neglecting the Sitarz term, we can make the following predictions. The first model deduces the inequality m_H≤√<2>m_w, whereas the second model leads to the interesting relation m_H=2√<2>m_wsinθ_w. This implies m_H=109.1 GeV if we take sin^2 θ_w=0.233 and m_w=79.9 GeV as the experimental values.
理論物理学刊行会の論文
1994-09-25