New Incorporation of the Strong Interaction in NCG and Standard Model

概要

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The standard model is reconstructed by a new method to incorporate strong interaction into our previous schime based on non-commutative geometry. Generation mixing is also taken into account. The characteristic feature is to take the fermion diels so as to contain quarks and leptons all together which is almost equal to that of the SO(10) grand unifked theory (GUT). The space-time M_4×Z_2; Minkowski space multiplied by a two point discrete space is prepared to express the left-handed and right-handed fermionfields. The generalized gauge field A(x,y) written in one-differential form extended on M_4×Z_2 is built to give the correct Dirac Lagrangian for the fermion sector. The fermion field is a vector in 24-dimensional space. Gauge and Higgs fields are written as 24×24 matrices. At the energy of equal coupling constants for both sheets y = ± expected to be the energy of the GUT scale, we obtain sin^2θ_W = 3/8 and m_H = √<2>m_W. In general, the equation m_H = (4/√<3>)m_Wsinθ_W is followed. Then, it should be noted that the same result as that of the grand unified theory such as SU(5) and SO(10) GUTs is obtained without GUT but with an approach based on non-commutative geometry. In addition, the Higgs mass is related to other physical quantities as stated above.
理論物理学刊行会の論文
1996-05-25