The Noncommutative Geometry of the Standard Model

Cottingham, W.N., Greenwood, D.A.: An Introduction to the Standard Model of Particle Physics, 2nd edn. Cambridge University Press, Cambridge (2007)CrossRefzbMATHGoogle Scholar

Kane, G.L.: Modern Elementary Particle Physics. Perseus, Cambridge (1993)Google Scholar

Connes, A.: Gravity coupled with matter and the foundation of non-commutative geometry. Commun. Math. Phys. 182, 155–176 (1996)ADSCrossRefzbMATHMathSciNetGoogle Scholar

Connes, A.: Essay on physics and noncommutative geometry. In: The Interface of Mathematics and Particle Physics (Oxford, 1988), The Institute of Mathematics and its Applications Conference Series, vol. 24, pp. 9–48. Oxford University Press, New York (1990)Google Scholar

Connes, A., Lott, J.: Particle models and noncommutative geometry. Nucl. Phys. Proc. Suppl. 18B, 29–47 (1991)ADSCrossRefMathSciNetGoogle Scholar

Martín, C.P., Gracia-Bondía, J.M., Várilly, J.C.: The standard model as a noncommutative geometry: the low-energy regime. Phys. Rep. 294, 363–406 (1998)ADSCrossRefMathSciNetGoogle Scholar

Chamseddine, A.H., Connes, A.: Universal formula for noncommutative geometry actions: unifications of gravity and the standard model. Phys. Rev. Lett. 77, 4868–4871 (1996)ADSCrossRefzbMATHMathSciNetGoogle Scholar

Chamseddine, A.H., Connes, A.: The spectral action principle. Commun. Math. Phys. 186, 731–750 (1997)ADSCrossRefzbMATHMathSciNetGoogle Scholar

Scheck, F., Upmeier, H., Werner, W. (eds.): Noncommutative geometry and the standard model of elementary particle physics. Lecture Notes in Physics, vol. 596. Springer, Berlin (2002) (Papers from the conference held in Hesselberg, March 14–19, 1999)Google Scholar

Chamseddine, A.H., Connes, A., Marcolli, M.: Gravity and the standard model with neutrino mixing. Adv. Theor. Math. Phys. 11, 991–1089 (2007)CrossRefzbMATHMathSciNetGoogle Scholar

Barrett, J.W.: A Lorentzian version of the non-commutative geometry of the standard model of particle physics. J. Math. Phys. 48, 012303 (2007)ADSCrossRefMathSciNetGoogle Scholar

Connes, A.: Noncommutative geometry and the standard model with neutrino mixing. JHEP 0611, 081 (2006)ADSCrossRefMathSciNetGoogle Scholar

Lizzi, F., Mangano, G., Miele, G., Sparano, G.: Fermion Hilbert space and fermion doubling in the noncommutative geometry approach to gauge theories. Phys. Rev. D55, 6357–6366 (1997)ADSMathSciNetGoogle Scholar

Connes, A., Marcolli, M.: Noncommutative Geometry. Quantum Fields and Motives. AMS, Providence (2008)Google Scholar

van den Dungen, K., van Suijlekom, W.D.: Particle physics from almost commutative spacetimes. Rev. Math. Phys. 24, 1230004 (2012)CrossRefMathSciNetGoogle Scholar

Chamseddine, A.H., Connes, A.: Why the standard model. J. Geom. Phys. 58, 38–47 (2008)ADSCrossRefzbMATHMathSciNetGoogle Scholar

Ćaćić, B.: Moduli spaces of dirac operators for finite spectral triples. In: Marcolli, M., Parashar, D. (eds.) Quantum Groups and Noncommutative Spaces: Perspectives on Quantum Geometry. Vieweg Verlag, Wiesbaden (2010)Google Scholar

Alvarez, E., Gracia-Bondía, J.M., Martin, C.: Anomaly cancellation and the gauge group of the standard model in NCG. Phys. Lett. B364, 33–40 (1995)ADSCrossRefGoogle Scholar

Baez, J., Huerta, J.: The algebra of grand unified theories. Bull. Amer. Math. Soc. (N.S.) 47, 483–552 (2010)CrossRefzbMATHMathSciNetGoogle Scholar

Englert, F., Brout, R.: Broken symmetry and the mass of gauge vector mesons. Phys. Rev. Lett. 13, 321–323 (1964)ADSCrossRefMathSciNetGoogle Scholar

Higgs, P.W.: Broken symmetries and the masses of gauge bosons. Phys. Rev. Lett. 13, 508–509 (1964)ADSCrossRefMathSciNetGoogle Scholar

Weinberg, S.: Physical processes in a convergent theory of the weak and electromagnetic interactions. Phys. Rev. Lett. 27, 1688–1691 (1971)ADSCrossRefGoogle Scholar

Weinberg, S.: General theory of broken local symmetries. Phys. Rev. D7, 1068–1082 (1973)ADSGoogle Scholar

Weinberg, S.: The quantum theory of fields, vol. 2. Cambridge University Press, Cambridge (1996)Google Scholar