4 research outputs found
Connes' interpretation of the Standard Model and massive neutrinos
Massive neutrinos can be accommodated into the noncommutative geometry
reinterpretation of the Standard Model. The constrained Standard Model
Lagrangian is computed anew under the assumption of nonzero neutrino masses.
This gives the ``prediction" of a mass for the Higgs particle somewhat higher
than in the vanishing neutrino mass case.Comment: Final version, to appear in Phys Lett
Anomaly Cancellation and gauge group of the standard model in NCG
It is well known that anomaly cancellation {\it almost} determines the
hypercharges in the standard model. A related (and somewhat more stronger)
phenomenon takes place in Connes' NCG framework: unimodularity (a technical
condition on elements of the algebra) is {\it strictly} equivalent to anomaly
cancellation (in the absence of right-handed neutrinos); and this in turn
reduces the symmetry group of the theory to the standard .Comment: 10 pages, plain TeX.(TeX errors fixed
Connes' Tangent Groupoid and Strict Quantization
We address one of the open problems in quantization theory recently listed by
Rieffel. By developping in detail Connes' tangent groupoid principle and using
previous work by Landsman, we show how to construct a strict, flabby
quantization, which is moreover an asymptotic morphism and satisfies the
reality and traciality constraints, on any oriented Riemannian manifold. That
construction generalizes the standard Moyal rule. The paper can be considered
as an introduction to quantization theory from Connes' point of view.Comment: LaTeX file, 22 pages (elsart.cls required). Minor changes. Final
version to appear in J. Geom. and Phy
The Standard Model as a noncommutative geometry: the low energy regime
We render a thorough, physicist's account of the formulation of the Standard
Model (SM) of particle physics within the framework of noncommutative
differential geometry (NCG). We work in Minkowski spacetime rather than in
Euclidean space. We lay the stress on the physical ideas both underlying and
coming out of the noncommutative derivation of the SM, while we provide the
necessary mathematical tools. Postdiction of most of the main characteristics
of the SM is shown within the NCG framework. This framework, plus standard
renormalization technique at the one-loop level, suggest that the Higgs and top
masses should verify 1.3 m_top \lesssim m_H \lesssim 1.73 m_top.Comment: 44 pages, Plain TeX with AMS fonts, mass formulae readjusted, some
references added, to appear in Physics Report