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We review the noncommutative approach to the standard model.
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A. Connes and J. Lott, “Particle Models and Noncommutative Geometry (Expanded Version),” Nucl. Phys. Proc. Suppl. 18B
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A. Connes, Noncommutative Geometry
1994
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S. Doplicher, K. Fredenhagen and J. E. Roberts, “The Quantum structure of space-time at the Planck scale and quantum fields,” Commun. Math. Phys. 172
1995
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A. Connes, “Noncommutative geometry and reality,” J. Math. Phys. 36
1995
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A. H. Chamseddine and A. Connes, “Universal formula for noncommutative geometry actions: Unification of gravity and the standard model,” Phys. Rev. Lett. 77
1996
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F. Lizzi, G. Mangano, G. Miele and G. Sparano, “Constraints on unified gauge theories from noncommutative geometry,” Mod. Phys. Lett. A 11
1996
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G. Landi, “An Introduction to noncommutative spaces and their geometry,” Lect. Notes Phys. Monogr. 51
1997
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A. H. Chamseddine and A. Connes, “The Spectral action principle,” Commun. Math. Phys. 186
1997
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F. Lizzi, G. Mangano, G. Miele and G. Sparano, “Fermion Hilbert space and fermion doubling in the noncommutative geometry approach to gauge theories,” Phys. Rev. D 55
1997
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F. Lizzi, G. Mangano, G. Miele and G. Sparano, “Mirror fermions in noncommutative geometry,” Mod. Phys. Lett. A 13
1998
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J. M. Gracia-Bondia, B. Iochum and T. Schucker, “The Standard model in noncommutative geometry and fermion doubling,” Phys. Lett. B 416
1998
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J.M. Gracia-Bondia, J. Varilly, H. Figueroa, Elements of Noncommutative Geometry
2000
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S. Minwalla, M. Van Raamsdonk and N. Seiberg, “Noncommutative perturbative dynamics,” JHEP 0002
2000
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S. Doplicher, “Space-time and fields: A Quantum texture,” AIP Conf. Proc. 589
2001
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M. Visser, “Sakharov’s induced gravity: A Modern perspective,” Mod. Phys. Lett. A 17
2002
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D. V. Vassilevich, “Heat kernel expansion: User’s manual,” Phys. Rept. 388
2003
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V. Moretti, “Aspects of noncommutative Lorentzian geometry for globally hyperbolic space-times,” Rev. Math. Phys. 15
2003
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G. Esposito, G. Marmo and E. C. G. Sudarshan, From Classical to Quantum Mechanics
2004
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K. Fujikawa, H. Suzuki. Path Integrals And Quantum Anomalies
2004
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M. Paschke and R. Verch, “Local covariant quantum field theory over spectral geometries,” Class. Quant. Grav. 21
2004
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F. Lizzi, P. Vitale and A. Zampini, “The fuzzy disc: A review,” J. Phys. Conf. Ser. 53
2006
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A. Strohmaier, “On noncommutative and semi-Riemannian geometry,” J. Geom. Phys. 56
2006
Cited alongside, same era.
A. Connes, M. Marcolli, Noncommutative Geometry, Quantum Fields and Motives
2007
Cited alongside, same era.
A. H. Chamseddine, A. Connes and M. Marcolli, “Gravity and the standard model with neutrino mixing,” Adv. Theor. Math. Phys. 11
2007
Cited alongside, same era.
2007
Cited alongside, same era.
J.W. Barrett, “A Lorentzian version of the non-commutative geometry of the standard model of particle physics,” J. Math. Phys. 48
2007
Cited alongside, same era.
2014
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A. Devastato, F. Lizzi and P. Martinetti, “Higgs mass in Noncommutative Geometry,” Fortsch. Phys. 62
2014
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N. Franco and M. Eckstein, “Exploring the Causal Structures of Almost Commutative Geometries,” SIGMA 10
2014
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2014
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W. Van Suijlekom, Noncommutative Geometry and Particle Physics
2015
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A. Connes and H. Moscovici, “Type III and spectral triples”, Traces in number theory, geo. and quantum fields, Aspects Math. E38 (2008), no. Friedt. Vieweg, Wiesbaden, 57-71
2008
Cited alongside, same era.
P. Aschieri, M. Dimitrijevic, P. Kulish, F. Lizzi and J. Wess, Noncommutative spacetimes: Symmetries in noncommutative geometry and field theory,
2009
Cited alongside, same era.
C. A. Stephan, “New Scalar Fields in Noncommutative Geometry,” Phys. Rev. D 79
2009
Cited alongside, same era.
2009
Cited alongside, same era.
2010
Cited alongside, same era.
A. A. Andrianov, M. A. Kurkov and F. Lizzi, “Spectral Action from Anomalies,” PoS CNCFG 2010
2010
Cited alongside, same era.
2010
Cited alongside, same era.
2015
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2015
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2015
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2015
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U. Aydemir, D. Minic, C. Sun and T. Takeuchi, “Higgs mass, superconnections, and the TeV-scale left-right symmetric model,” Phys. Rev. D 91
2015
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2015
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F. Canfora, M. Kurkov, L. Rosa and P. Vitale, “The Gribov problem in Noncommutative QED,” JHEP 1601
2016
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2016
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U. Aydemir, D. Minic, C. Sun and T. Takeuchi, “PatiÐSalam unification from noncommutative geometry and the TeV-scale W R W_{R} boson,” Int. J. Mod. Phys. A 31
2016
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2016
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K. Dungen, “Krein Spectral Triples and the Fermionic Action,” Math. Phys. Anal. Geom. 19
2016
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2016
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2017
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2017
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2017
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H. Karimi, “Implications of the complex Singlet field for Noncommutative Geometry model,” JHEP 1712
2017
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2017
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M. Kurkov and D. Vassilevich, “Parity anomaly in four dimensions,” Phys. Rev. D 96
2017
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M. Kurkov and P. Vitale, “The Gribov problem in Noncommutative gauge theory,” Int. J. Geom. Meth. Mod. Phys. 15
2018
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2018
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2018
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M. Kurkov and D. Vassilevich, “Gravitational parity anomaly with and without boundaries,” JHEP 1803
2018
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