Noncommutative standard model

Noncommutative Standard Model

Noncommutative standard model

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In theoretical particle physics, the non-commutative Standard Model, mainly due to the French mathematician Alain Connes, uses his noncommutative geometry to devise an extension of the Standard Model to include a modified form of general relativity. This unification implies a few constraints on the parameters of the Standard Model. Under an additional assumption, known as the "big desert" hypothesis, one of these constraints determines the mass of the Higgs boson to be around 170 GeV, comfortably within the range of the Large Hadron Collider. Recent Tevatron experiments exclude a Higgs mass of 158 to 175 GeV at the 95% confidence level.


Current physical theory features four elementary forces: the gravitational force, the electromagnetic force, the weak force, and the strong force. Gravity has an elegant and experimentally precise theory: Einstein's general relativity. It is based on Riemannian geometry and interprets the gravitational forceas curvature of space-time. Its Lagrangian formulation requires only two empirical parameters, the gravitational constant and the cosmological constant.

The other three forces also have a Lagrangian theory, called the Standard Model. Its underlying idea is that they are mediated by the exchange of spin-1 particles, the so-called gauge bosons. The one responsible for electromagnetism is the photon. The weak force is mediated by the W and Z bosons; the strong force, by......
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