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Prog. Theor. Phys. Vol. 95 No. 5 (1996) pp. 969-984

[ Full Text PDF : FREE ACCESS (738K) ]

New Incorporation of the Strong Interaction in NCG and Standard Model

Yoshitaka Okumura

Department of Natural Science, Chubu University, Kasugai 487

(Received November 1, 1995)

Abstract:

The standard model is reconstructed by a new method to incorporate strong interaction into our previous scheme based on non-commutative geometry. Generation mixing is also taken into account. The characteristic feature is to take the fermion field so as to contain quarks and leptons all together which is almost equal to that of the SO(10) grand unified theory (GUT). The space-time M4 ×Z2; Minkowski space multiplied by a two point discrete space is prepared to express the left-handed and right-handed fermion fields. The generalized gauge field A(x, y) written in one-differential form extended on M4 ×Z2 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 2θW = 3/8 and m_H = \sqrt2m_W. In general, the equation m_H = (4/\sqrt3)m_W sin θ_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.


URL : http://ptp.ipap.jp/link?PTP/95/969/
DOI : 10.1143/PTP.95.969

[ Full Text PDF : FREE ACCESS (738K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 96 No. 5 (1996) pp. 1021-1035 :
    Non-Commutative Differential Geometry on Discrete Space M4 ×ZN and Gauge Theory
    Yoshitaka Okumura
  2. Progress of Theoretical Physics Vol. 97 No. 3 (1997) pp. 491-506 :
    Two Higgs Doublet Model in a Noncommutative Geometry on the Discrete Space M4 ×Z4
    Yoshitaka Okumura
  3. Progress of Theoretical Physics Vol. 98 No. 1 (1997) pp. 187-209 :
    Fine-Tuning Problem in a Left-Right Symmetric Model and Sogami's Generalized Covariant Derivative Method
    Eizou Umezawa
  4. Progress of Theoretical Physics Vol. 98 No. 6 (1997) pp. 1333-1344 :
    Renormalization Group Analysis of the Higgs Boson Mass in a Noncommutative Geometry
    Yoshitaka Okumura
  5. Progress of Theoretical Physics Vol. 100 No. 2 (1998) pp. 375-394 :
    Constraints among Coupling Constants in Noncommutative Geometry Models
    Eizou Umezawa

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