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Prog. Theor. Phys. Vol. 67 No. 6 (1982) pp. 1860-1876

[ Full Text PDF : FREE ACCESS (670K) ]

Quaternionic Weinberg-Salam Theory

Katsusada Morita

Department of Physics, Faculty of Science, Nagoya University, Nagoya 464

(Received September 12, 1981; Revised December 21, 1981)

Abstract:

A quaternionic Weinberg-Salam theory is formulated based on the assumption that fermions and Higgs mesons are defined over quaternions. The new formalism, reproducing the left-right symmetric SU(2)L×SU(2)R×U(1) Weinberg-Salam theory at the phenomenological level, offers an algebraic explanation for replication of quarks and leptons in flavor doublets, and correlates the spontaneous symmetry breakdown to U(1)em with the existence of Fock space for gauge singlets but not for quaternionic states. In particular, the quaternionic variational principle is introduced to canonically quantize the quaternionic fields in conformity with the gauge-singlet Fock-space formulation and the spontaneous symmetry breakdown. Physical states must be gauge singlets since they belong to the Fock space.


URL : http://ptp.ipap.jp/link?PTP/67/1860/
DOI : 10.1143/PTP.67.1860

[ Full Text PDF : FREE ACCESS (670K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 68 No. 6 (1982) pp. 2159-2175 :
    Algebraic Gauge Theory of Quarks and Leptons
    Katsusada Morita
  2. Progress of Theoretical Physics Vol. 70 No. 6 (1983) pp. 1648-1665 :
    Quaternionic Formulation of Dirac Theory in Special and General Relativity
    Katsusada Morita
  3. Progress of Theoretical Physics Vol. 85 No. 1 (1991) pp. 157-168 :
    Quaternion Gauge Theory of Dyonic Fields
    P. S. Bisht, O. P. S. Negi and B. S. Rajput
  4. Progress of Theoretical Physics Vol. 90 No. 1 (1993) pp. 219-236 :
    Quaternions and Non-Commutative Geometry
    Katsusada Morita
  5. Progress of Theoretical Physics Vol. 92 No. 5 (1994) pp. 917-926 :
    Translations between Quaternion and Complex Quantum Mechanics
    S. De Leo and P. Rotelli
  6. Progress of Theoretical Physics Vol. 94 No. 6 (1995) pp. 1109-1120 :
    Duffin-Kemmer-Petiau Equation on the Quaternion Field
    Stefano De Leo
  7. Progress of Theoretical Physics Vol. 95 No. 6 (1996) pp. 1029-1039 :
    Half-Whole Dimensions in Quaternionic Quantum Mechanics
    Stefano De Leo
  8. Progress of Theoretical Physics Vol. 96 No. 4 (1996) pp. 833-845 :
    Octonionic Dirac Equation
    Stefano De Leo and Khaled Abdel-Khalek

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