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| In theoretical ], the '''non-commutative Standard Model''', mainly due to the French mathematician ], uses his ] to devise an extension of the ] to include a modified form of ]. 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 ] to be around 170 ], comfortably within the range of the ]. Recent ] experiments exclude a Higgs mass of 158 to 175 GeV at the 95% confidence level and recent experiments at ] suggest a Higgs mass of between 125 GeV and 127 GeV.<ref name="CERN March 2013">{{cite web|last=Pralavorio|first=Corinne|title=New results indicate that new particle is a Higgs boson|url=http://home.web.cern.ch/about/updates/2013/03/new-results-indicate-new-particle-higgs-boson|accessdate=14 March 2013|date=2013-03-14|publisher=CERN}}</ref><ref name=nbc14032013>{{cite news |last=Bryner |first=Jeanna |title=Particle confirmed as Higgs boson |url=http://science.nbcnews.com/_news/2013/03/14/17311477-particle-confirmed-as-higgs-boson |date=14 March 2013 |work=] |accessdate=14 March 2013}}</ref><ref name="Huffington 14 March 2013">{{cite news|url=http://www.huffingtonpost.com/2013/03/14/higgs-boson-discovery-confirmed-cern-large-hadron-collider_n_2874975.html?icid=maing-grid7%7Cmain5%7Cdl1%7Csec1_lnk2%26pLid%3D283596|title= Higgs Boson Discovery Confirmed After Physicists Review Large Hadron Collider Data at CERN|publisher= Huffington Post|accessdate=14 March 2013|date=14 March 2013}}</ref> However, the previously computed Higgs mass was found to have an error, and more recent calculations are in line with the measured Higgs mass.<ref></ref><ref>Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models </ref> | In theoretical ], the '''non-commutative Standard Model''', mainly due to the French mathematician ], uses his ] to devise an extension of the ] to include a modified form of ]. 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 ] to be around 170 ], comfortably within the range of the ]. Recent ] experiments exclude a Higgs mass of 158 to 175 GeV at the 95% confidence level and recent experiments at ] suggest a Higgs mass of between 125 GeV and 127 GeV.<ref name="CERN March 2013">{{cite web|last=Pralavorio|first=Corinne|title=New results indicate that new particle is a Higgs boson|url=http://home.web.cern.ch/about/updates/2013/03/new-results-indicate-new-particle-higgs-boson|accessdate=14 March 2013|date=2013-03-14|publisher=CERN}}</ref><ref name=nbc14032013>{{cite news |last=Bryner |first=Jeanna |title=Particle confirmed as Higgs boson |url=http://science.nbcnews.com/_news/2013/03/14/17311477-particle-confirmed-as-higgs-boson |date=14 March 2013 |work=] |accessdate=14 March 2013}}</ref><ref name="Huffington 14 March 2013">{{cite news|url=http://www.huffingtonpost.com/2013/03/14/higgs-boson-discovery-confirmed-cern-large-hadron-collider_n_2874975.html?icid=maing-grid7%7Cmain5%7Cdl1%7Csec1_lnk2%26pLid%3D283596|title= Higgs Boson Discovery Confirmed After Physicists Review Large Hadron Collider Data at CERN|publisher= Huffington Post|accessdate=14 March 2013|date=14 March 2013}}</ref> However, the previously computed Higgs mass was found to have an error, and more recent calculations are in line with the measured Higgs mass.<ref></ref><ref>Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models </ref> | ||
| ==Background== | |||
| Current physical theory features four ]: the ], the ], the ], and the ]. Gravity has an elegant and experimentally precise theory: ]'s ]. It is based on ] and interprets the gravitational force | |||
| as curvature of ]. Its ] formulation requires only two empirical parameters, the ] and the ]. | |||
| The other three forces also have a Lagrangian theory, called the ]. Its underlying idea is that they are mediated by the exchange of ]-1 particles, the so-called ]. The one responsible for electromagnetism is the ]. The weak force is mediated by the ]; the strong force, by ]s. The gauge Lagrangian is much more complicated than the gravitational one: at present, it involves some 30 real parameters, a number that could increase. What is more, the gauge Lagrangian must also contain a ] 0 particle, the ], to give mass to the spin 1/2 and spin 1 particles. | |||
| ] has generalized ]'s geometry to ]. It | |||
| describes spaces with curvature and uncertainty. Historically, the first example of such a geometry is ], which introduced ]'s ] by turning the classical observables of position and momentum into noncommuting operators. Noncommutative geometry is still sufficiently similar to ] that Connes was able to rederive ]. In doing so, he obtained the gauge ] as a companion of the gravitational one, a truly geometric unification of all four ]s. Connes has thus devised a fully geometric formulation of the ], where all the parameters are geometric invariants of a noncommutative space. A result is that parameters like the ] are now analogous to purely mathematical constants like ]. In 1929 Weyl wrote Einstein that any unified theory would need to include the metric tensor, a gauge field, and a matter field. Einstein considered the Einstein-Maxwell-Dirac system by 1930. He probably didn't develop it because he was unable to geometricize it. It can now be geometricized as a non-commutative geometry. | |||
| It is worth stressing that, however, a fundamental physical drawback plagues this interesting and very remarkable attempt. Barring some relevant partial results, all the noncommutative geometry structure is a generalization of Riemannian geometry, that is a geometry where the ] is positively defined. Conversely physics deals with the geometric structure known as ] that allows one to give a mathematically rigorous description of ]. | |||
| In particular cases (in presence of a ] ] field in the Lorentzian picture) one passes from the Riemannian picture to the Lorentzian (pseudo-Riemannian) one by means of the so-called ], without loss of information. Up to now no generalization of the Wick rotation exists in the noncommutative case. | |||
| ==See also== | ==See also== | ||
Revision as of 17:56, 9 December 2018
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 and recent experiments at CERN suggest a Higgs mass of between 125 GeV and 127 GeV. However, the previously computed Higgs mass was found to have an error, and more recent calculations are in line with the measured Higgs mass.
See also
- Noncommutative geometry
- Noncommutative quantum field theory
- Timeline of atomic and subatomic physics
Notes
- Pralavorio, Corinne (2013-03-14). "New results indicate that new particle is a Higgs boson". CERN. Retrieved 14 March 2013.
- Bryner, Jeanna (14 March 2013). "Particle confirmed as Higgs boson". NBC News. Retrieved 14 March 2013.
- "Higgs Boson Discovery Confirmed After Physicists Review Large Hadron Collider Data at CERN". Huffington Post. 14 March 2013. Retrieved 14 March 2013.
- Resilience of the Spectral Standard Model
- Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models
References
- Alain Connes (1994) Noncommutative geometry. Academic Press. ISBN 0-12-185860-X.
- -------- (1995) "Noncommutative geometry and reality," J. Math. Phys. 36: 6194.
- -------- (1996) "Gravity coupled with matter and the foundation of noncommutative geometry," Comm. Math. Phys. 155: 109.
- -------- (2006) "Noncommutative geometry and physics,"
- -------- and M. Marcolli, Noncommutative Geometry: Quantum Fields and Motives. American Mathematical Society (2007).
- Chamseddine, A., A. Connes (1996) "The spectral action principle," Comm. Math. Phys. 182: 155.
- Chamseddine, A., A. Connes, M. Marcolli (2007) "Gravity and the Standard Model with neutrino mixing," Adv. Theor. Math. Phys. 11: 991.
- Jureit, Jan-H., Thomas Krajewski, Thomas Schücker, and Christoph A. Stephan (2007) "On the noncommutative standard model," Acta Phys. Polon. B38: 3181-3202.
- Schücker, Thomas (2005) Forces from Connes's geometry. Lecture Notes in Physics 659, Springer.