Weinberg-Salam Theory in Non-Commutative Geometry : Particles and Fields

概要

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Ordinary differential calculus on smooth manifold is generalized so as to construct gauge theory coupled to fermions on discrete space M_4×Z_ 2 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 m_H=√<2>m_W. The first model leaves the Weinberg angle arbitrary as usual, while the second one predicts sin^2θ_W=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.
理論物理学刊行会の論文
1994-05-25