Prog. Theor. Phys. Vol. 94 No. 6 (1995) pp. 1121-1133
Modified Reconstruction of Standard Model in Non-Commutative Differential Geometry
Department of Natural Science, Chubu University, Kasugai 487
*Department of Physics, Nagoya University, Nagoya 464-01
(Received July 13, 1995)
Sogami recently proposed the new idea to express Higgs particle as a kind of gauge particle by prescribing the generalized covariant derivative with gauge and Higgs fields operating on quark and lepton fields. The field strengths for both the gauge and Higgs fields are defined by the commutators of the covariant derivative by which he could obtain the Yang-Mills Higgs Lagrangian in the standard model. Inspired by Sogami's work, we present a modification of our previous scheme to formulate the spontaneously broken gauge theory in non-commutative geometry on the discrete space M4 ×Z2 by introducing the generation mixing matrix K in dχ operation on the fields ai(x, y) which compose the gauge and Higgs fields. The standard model is reconstructed according to the modified scheme, which does not yield not only any special relations between the particle masses but also the special restriction on the Higgs potential.
DOI : 10.1143/PTP.94.1121
- A. Connes, in The Interface of Mathematics and Particle Physics, ed. D. G. Quillen, G. B. Segal and S. T. Tsou (Clarendon Press, Oxford, 1990), p. 9.
See also, A. Connes and J. Lott, Nucl. Phys. B (Proc. Suppl.) 18B (1990), 57.
- A. H. Chamseddine, G. Felder and J. Frölich, Phys. Lett. B296 (1992), 109; Nucl. Phys. B395 (1993), 672.
A. H. Chamseddine and J. Frölich, Phys. Rev. D50 (1994), 2893[APS].
- D. Kastler, Rev. Math. Phys. 5 (1993), 477.
M. Dubois-Violette, Class. Quantum. Grav. 6 (1989), 1709[CrossRef].
R. Coquereaux, G. Esposito-Farese and G. Vaillant, Nucl. Phys. B353 (1991), 689.
M. Dubois-Violette, R. Kerner and J. Madore, J. Math. Phys. 31 (1990), 316[CrossRef].
B. Balakrishna, F. Gürsey and K. C. Wali, Phys. Lett. B254 (1991), 430;
Phys. Rev. D46 (1992), 6498[APS].
R. Coquereaux, G. Esposito-Farese and F. Scheck, Int. J. Mod. Phys. A7 (1992), 6555.
R. Coquereaux, R. Haussling, N. Papadopoulos and F. Scheck, ibid 7 (1992), 2809.
- A. Sitarz, Phys. Lett. B308 (1993), 311; Jour. Geom. Phys. 15 (1995), 123.
- H-G. Ding, H-Y. Gou, J-M. Li and K. Wu, Preprint, ASITP-93-23, CCAST-93-5.
K. Morita and Y. Okumura, Phys. Rev. D50 (1994), 1016[APS].
Y. Okumura, Prog. Theor. Phys. 92 (1994), 625[PTP].
- K. Morita and Y. Okumura, Prog. Theor. Phys. 91 (1994), 975[PTP].
Y. Okumura, Phys. Rev. D50 (1994), 1026[APS].
- K. Morita and Y. Okumura, Prog. Theor. Phys. 91 (1994), 959[PTP].
- K. Morita and Y. Okumura, Prog. Theor. Phys. 93 (1995), 545[PTP].
- S. Naka and E. Umezawa, Prog. Theor. Phys. 92 (1994), 189[PTP].
- M. V. Berry, Proc. R. Soc. London A392 (1984), 45.
- Y. Okumura, Prog. Theor. Phys. 94 (1995), 607[PTP].
- I. S. Sogami, Prog. Theor. Phys. 94 (1995), 117[PTP].
- G. Konisi and T. Saito, Prog. Theor. Phys. 93 (1995), 1093[PTP].
Citing Article(s) :
Progress of Theoretical Physics Vol. 95 No. 5 (1996) pp. 969-984
New Incorporation of the Strong Interaction in NCG and Standard Model
Progress of Theoretical Physics Vol. 96 No. 5 (1996) pp. 1021-1035
Non-Commutative Differential Geometry on Discrete Space M4 ×ZN and Gauge Theory
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
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