109 research outputs found
Non-Commutative Differential Geometry and Standard Model
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; four dimensinal Minkovski space multiplyed by two point discrete
space. 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. The proof is given for
a single Higgs 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 the discrete space-time.Comment: 27 page
Lorentz Invariance And Unitarity Problem In Non-Commutative Field Theory
It is shown that the one-loop two-point amplitude in {\it Lorentz-invariant}
non-commutative (NC) theory is finite after subtraction in the
commutative limit and satisfies the usual cutting rule, thereby eliminating the
unitarity problem in Lorentz-non-invariant NC field theory in the approximation
considered.Comment: 14 page
Lagrangian Formulation of Connes' Gauge Theory
It is shown that Connes' generalized gauge field in non-commutative geometry
is derived by simply requiring that Dirac lagrangian be invariant under local
transformations of the unitary elements of the algebra, which define the gauge
group. The spontaneous breakdown of the gauge symmetry is guaranteed provided
the chiral fermions exist in more than one generations as first observed by
Connes-Lott. It is also pointed out that the most general gauge invariant
lagrangian in the bosonic sector has two more parameters than in the original
Connes-Lott scheme.Comment: 9 pages, PTPTEX.st
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