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Prog. Theor. Phys. Vol. 95 No. 1 (1996) pp. 227-248

[ Full Text PDF : FREE ACCESS (922K) ]

Non-Commutative Differential Geometry and Standard Model

Katsusada Morita and Yoshitaka Okumura*

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

(Received August 14, 1995)

Abstract:

We incorporate Sogami's idea in the standard model into our previous formulation of non-commutative differential geometry by extending the action of the extra exterior derivative operator on spinors defined over the discrete space-time M4 ×Z2. The extension consists in making it possible to require that the operator become nilpotent when acting on the spinors. It is shown that the generalized field strength leads to the most general, gauge-invariant Yang-Mills-Higgs lagrangian even if the extra exterior derivative operator is not nilpotent, while the fermionic part remains intact. A proof is given for a single Higs model. The method is applied to reformulate the standard model by putting left-handed fermion doublets on the upper sheet and right-handed fermion singlets on the lower sheet with generation mixing among quarks being taken into account. We also present a matrix calculus of the method without referring to discrete space-time.


URL : http://ptp.ipap.jp/link?PTP/95/227/
DOI : 10.1143/PTP.95.227

[ Full Text PDF : FREE ACCESS (922K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 96 No. 4 (1996) pp. 787-799 :
    Super Yang-Mills Theories and Non-Commutative Geometry
    Katsusada Morita
  2. Progress of Theoretical Physics Vol. 96 No. 4 (1996) pp. 801-821 :
    Connes' Gauge Theory and the Clifford Product
    Katsusada Morita
  3. Progress of Theoretical Physics Vol. 96 No. 6 (1996) pp. 1179-1187 :
    Renormalization Group Effects on the Mass Relation Predicted by the Standard Model with Generalized Covariant Derivatives
    Tadatomi Shinohara, Kouzou Nishida, Hajime Tanaka and Ikuo S. Sogami
  4. 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

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