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Prog. Theor. Phys. Vol. 91 No. 5 (1994) pp. 959-974

[ Full Text PDF : FREE ACCESS (1452K) ]

Weinberg-Salam Theory in Non-Commutative Geometry

Katsusada Morita and Yoshitaka Okumura*

Department of Physics, Nagoya University, Nagoya 464-01
*Department of Applied Physics, Chubu University, Kasugai 487

(Received July 28, 1993)

Abstract:

Ordinary differential calculus on smooth manifold is generalized so as to construct gauge theory coupled to fermions on discrete space M4 ×Z2 which is an underlying space-time in the non-commutative geometry for the standard model. We can reproduce not only the bosonic sector but also the fermionic sector of the Weinberg-Salam theory without recourse to the Dirac operator at the outset. Treatment of the fermionic sector is based on the generalized spinor one-forms from which the Dirac lagrangian is derived through taking the inner product. Two model constructions are presented using our formalism, both giving the classical mass relation mH = √2mW. The first model leaves the Weinberg angle arbitrary as usual, while the second one predicts sin2θW = 1/4 in the tree level. This prediction is the same as that of Connes but we obtain it from correct hypercharge assignment of 2 ×2 matrix-valued Higgs field and from vanishing photon mass, thereby dispensing with Connes' 0-trace condition or the equivalent.


URL : http://ptp.ipap.jp/link?PTP/91/959/
DOI : 10.1143/PTP.91.959

[ Full Text PDF : FREE ACCESS (1452K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 91 No. 5 (1994) pp. 975-990 :
    Gauge Theory on Discrete Space M4 ×ZN and SU(5) GUT in Non-Commutative Geometry
    Katsusada Morita and Yoshitaka Okumura
  2. Progress of Theoretical Physics Vol. 92 No. 2 (1994) pp. 397-412 :
    Weinberg-Salam Theory Based on a Z2- Graded Algebra
    Jugoro Iizuka, Hiromi Kase, Katsusada Morita, Yositaka Okumura and Mieko Tanaka-Yamawaki
  3. Progress of Theoretical Physics Vol. 92 No. 3 (1994) pp. 625-643 :
    Standard Model in Differential Geometry on Discrete Space M4 ×Z3
    Yoshitaka Okumura
  4. Progress of Theoretical Physics Vol. 93 No. 3 (1995) pp. 621-629 :
    Brans-Dicke Theory and Discrete Symmetry
    Gaku Konisi, Takesi Saito and Ke Wu
  5. Progress of Theoretical Physics Vol. 93 No. 5 (1995) pp. 969-980 :
    Note on Two-Higgs-Doublets Model in Non-Commutative Differential Geometry
    Katsusada Morita and Yoshitaka Okumura
  6. Progress of Theoretical Physics Vol. 93 No. 6 (1995) pp. 1075-1091 :
    Unified Treatment of Gauge and Higgs Fields in Non-Commutative Differential Geometry
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  7. Progress of Theoretical Physics Vol. 93 No. 6 (1995) pp. 1093-1104 :
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  8. Progress of Theoretical Physics Vol. 94 No. 1 (1995) pp. 117-123 :
    Generalized Covariant Derivative with Gauge and Higgs Fields in the Standard Model
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  9. Progress of Theoretical Physics Vol. 94 No. 3 (1995) pp. 445-455 :
    Sogami's Generalized Covariant Derivative and Non-Commutative Differential Geometry
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  10. Progress of Theoretical Physics Vol. 94 No. 4 (1995) pp. 589-606 :
    Left-Right Symmetric Gauge Theory in Non-Commutative Geometry on M4 ×ZN
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  11. Progress of Theoretical Physics Vol. 94 No. 4 (1995) pp. 607-619 :
    SO(10) Grand Unified Theory in Non-Commutative Differential Geometry on the Discrete Space M4 ×ZN
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  12. Progress of Theoretical Physics Vol. 94 No. 6 (1995) pp. 1121-1133 :
    Modified Reconstruction of Standard Model in Non-Commutative Differential Geometry
    Yoshitaka Okumura, Shin-ichi Suzuki and Katsusada Morita
  13. Progress of Theoretical Physics Vol. 95 No. 1 (1996) pp. 227-248 :
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  14. Progress of Theoretical Physics Vol. 95 No. 3 (1996) pp. 637-655 :
    Minimal SU(5) Grand Unified Theory Based on Generalized Covariant Derivatives with Gauge and Higgs Fields
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  15. Progress of Theoretical Physics Vol. 95 No. 3 (1996) pp. 657-664 :
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  16. Progress of Theoretical Physics Vol. 95 No. 5 (1996) pp. 969-984 :
    New Incorporation of the Strong Interaction in NCG and Standard Model
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  17. Progress of Theoretical Physics Vol. 96 No. 4 (1996) pp. 787-799 :
    Super Yang-Mills Theories and Non-Commutative Geometry
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  18. Progress of Theoretical Physics Vol. 96 No. 4 (1996) pp. 801-821 :
    Connes' Gauge Theory and the Clifford Product
    Katsusada Morita
  19. Progress of Theoretical Physics Vol. 96 No. 6 (1996) pp. 1291-1299 :
    Brans-Dicke Theory on M4 ×Z2 Geometry
    Akira Kokado, Gaku Konisi, Takesi Saito and Kunihiko Uehara
  20. 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
  21. 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
  22. 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
  23. Progress of Theoretical Physics Vol. 100 No. 1 (1998) pp. 147-164 :
    Gauge Theories Coupled to Fermions in Generation
    Hiromi Kase, Katsusada Morita and Yoshitaka Okumura
  24. Progress of Theoretical Physics Vol. 100 No. 1 (1998) pp. 165-177 :
    Grand Unification from Gauge Theory in M4 ×ZN
    Masahiro Kubo, Ziro Maki, Mikio Nakahara and Takesi Saito
  25. Progress of Theoretical Physics Vol. 101 No. 5 (1999) pp. 1105-1118 :
    Left-Right Symmetric Model from Geometric Formulation of Gauge Theory in M4 ×Z2 ×Z2
    Gaku Konisi, Ziro Maki, Mikio Nakahara and Takesi Saito
  26. Progress of Theoretical Physics Vol. 103 No. 2 (2000) pp. 411-423 :
    Bi-Local Higgs-Like Fields Based on Non-Commutative Geometry
    Shigefumi Naka, Shinji Abe,* Eizou Umezawa and Tetsu Matsufuji
  27. Progress of Theoretical Physics Vol. 103 No. 3 (2000) pp. 621-634 :
    SO(10) Grand Unified Theory in Generalized Covariant Derivative Formalism
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  28. Progress of Theoretical Physics Vol. 109 No. 4 (2003) pp. 663-685 :
    Lorentz-Invariant Non-Commutative Space-Time Based on DFR Algebra
    Hiromi Kase, Katsusada Morita, Yoshitaka Okumura and Eizou Umezawa

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