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This is a survey of the historical development of the Spectral Standard Model and beyond, starting with the ground breaking paper of Alain Connes in 1988 where he observed that there is a link between Higgs fields and finite noncommutative spaces.
Clifford-based spectral action and renormalization group analysis of the gauge couplings
U. Aydemir · 1902
Earlier work this paper cites.
On the uniqueness of barrett’s solution to the fermion doubling problem in noncommutative geometry
F. Besnard · 1903
Earlier work this paper cites.
Second quantization and the spectral action
R. Dong and M. Khalkhali · 1903
Earlier work this paper cites.
Normal form of antiunitary operators
E. P. Wigner · 1960
Earlier work this paper cites.
Noncommutative differential geometry
A. Connes · 1985
Earlier work this paper cites.
Dérivations et calcul différentiel non commutatif
M. Dubois-Violette · 1988
Earlier work this paper cites.
Classical bosons in a noncommutative geometry
M. Dubois-Violette, R. Kerner, and J. Madore · 1989
Earlier work this paper cites.
Gauge bosons in a noncommutative geometry
M. Dubois-Violette, R. Kerner, and J. Madore · 1989
Earlier work this paper cites.
Essay on physics and noncommutative geometry
A. Connes · 1990
Earlier work this paper cites.
Noncommutative differential geometry and new models of gauge theory
M. Dubois-Violette, J. Madore, and R. Kerner · 1990
Earlier work this paper cites.
Particle models and noncommutative geometry
A. Connes and J. Lott · 1991
Earlier work this paper cites.
Unified gauge theories in noncommutative geometry
A. H. Chamseddine, G. Felder, and J. Fröhlich · 1992
Earlier work this paper cites.
Gravity in noncommutative geometry
A. H. Chamseddine, G. Felder, and J. Fröhlich · 1993
Earlier work this paper cites.
A detailed account of Alain Connes’ version of the standard model in noncommutative geometry. I, II
D. Kastler · 1993
Earlier work this paper cites.
Connes’ noncommutative differential geometry and the standard model
J. C. Várilly and J. M. Gracia-Bondía · 1993
Earlier work this paper cites.
Connection between space-time supersymmetry and noncommutative geometry
A. H. Chamseddine · 1994
Earlier work this paper cites.
Noncommutative Geometry
A. Connes · 1994
Earlier work this paper cites.
The gravitational sector in the Connes-Lott formulation of the standard model
A. H. Chamseddine, J. Fröhlich, and O. Grandjean · 1995
Earlier work this paper cites.
Noncommutative geometry and reality
A. Connes · 1995
Earlier work this paper cites.
An Introduction to Noncommutative Differential Geometry and its Physical Applications
J. Madore · 1995
Earlier work this paper cites.
Universal formula for noncommutative geometry actions: Unifications of gravity and the Standard Model
A. H. Chamseddine and A. Connes · 1996
Earlier work this paper cites.
A detailed account of Alain Connes’ version of the standard model in non-commutative differential geometry. III
D. Kastler · 1996
Earlier work this paper cites.
A detailed account of Alain Connes’ version of the standard model. IV
D. Kastler and T. Schücker · 1996
Earlier work this paper cites.
The standard model à la Connes-Lott
D. Kastler and T. Schücker · 1997
Earlier work this paper cites.
An Introduction to Noncommutative Spaces and their Geometry
G. Landi · 1997
Earlier work this paper cites.
Fermion Hilbert space and fermion doubling in the noncommutative geometry approach to gauge theories
F. Lizzi, G. Mangano, G. Miele, and G. Sparano · 1997
Cited alongside, same era.
A nonperturbative form of the spectral action principle in noncommutative geometry
H. Figueroa, J. M. Gracia-Bondía, F. Lizzi, and J. C. Várilly · 1998
Cited alongside, same era.
The standard model in noncommutative geometry and fermion doubling
J. M. Gracia-Bondía, B. Iochum, and T. Schücker · 1998
Cited alongside, same era.
Classification of finite spectral triples
T. Krajewski · 1998
Cited alongside, same era.
The standard model as a noncommutative geometry: the low-energy regime
C. P. Martín, J. M. Gracia-Bondía, and J. C. Várilly · 1998
Cited alongside, same era.
Discrete spectral triples and their symmetries
M. Paschke and A. Sitarz · 1998
Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
S. Chatrchyan et al · 2012
Later among the works it cites.
Beyond the spectral Standard Model: Emergence of Pati-Salam unification
A. H. Chamseddine, A. Connes, and W. D. van Suijlekom · 2013
Later among the works it cites.
Electrodynamics from noncommutative geometry
K. van den Dungen and W. D. van Suijlekom · 2013
Later among the works it cites.
Geometry and the quantum: Basics
A. H. Chamseddine, A. Connes, and V. Mukhanov · 2014
Later among the works it cites.
Higgs mass in noncommutative geometry
A. Devastato, F. Lizzi, and P. Martinetti · 2014
Later among the works it cites.
Grand symmetry, spectral action, and the Higgs mass
A. Devastato, F. Lizzi, and P. Martinetti · 2014
Later among the works it cites.
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Cited alongside, same era.
Noncommutative geometry and the standard model of elementary particle physics
F. Scheck, H. Upmeier, and W. Werner, editors · 1999
Cited alongside, same era.
Noncommutative geometry year 2000 [ MR1826266 (2003g:58010)]
A. Connes · 2002
Cited alongside, same era.
Unification and supersymmetry. The frontiers of quark-lepton physics
R. Mohapatra · 2003
Cited alongside, same era.
On a classification of irreducible almost commutative geometries
B. Iochum, T. Schucker, and C. Stephan · 2004
Cited alongside, same era.
On the foundations of noncommutative geometry
A. Connes · 2006
Cited alongside, same era.
Almost-commutative geometries beyond the Standard Model
C. A. Stephan · 2006
Cited alongside, same era.
A Dark Sector Extension of the Almost-Commutative Standard Model
C. A. Stephan · 2014
Later among the works it cites.
Quanta of geometry: Noncommutative aspects
A. H. Chamseddine, A. Connes, and V. Mukhanov · 2015
Later among the works it cites.
Grand unification in the spectral Pati-Salam model
A. H. Chamseddine, A. Connes, and W. D. van Suijlekom · 2015
Later among the works it cites.
Non-associative geometry and the spectral action principle
S. Farnsworth and L. Boyle · 2015
Later among the works it cites.
Noncommutative Geometry and Particle Physics
W. D. van Suijlekom · 2015
Later among the works it cites.
Pati–Salam unification from noncommutative geometry and the TeV-scale W R W_{R} boson
U. Aydemir, D. Minic, C. Sun, and T. Takeuchi · 2016
Later among the works it cites.
Supersymmetry and noncommutative geometry
W. Beenakker, T. van den Broek, and W. D. van Suijlekom · 2016
Later among the works it cites.
On twisting real spectral triples by algebra automorphisms
G. Landi and P. Martinetti · 2016
Later among the works it cites.
On noncommutative geometry of the Standard Model: fermion multiplet as internal forms
L. Dabrowski · 2017
Later among the works it cites.
Twisted spectral triple for the Standard Model and spontaneous breaking of the Grand Symmetry
A. Devastato and P. Martinetti · 2017
Later among the works it cites.
A new algebraic structure in the standard model of particle physics
L. Boyle and S. Farnsworth · 2018
Later among the works it cites.
The Standard Model in noncommutative geometry: fundamental fermions as internal forms
L. Dabrowski, F. D’Andrea, and A. Sitarz · 2018
Later among the works it cites.
Lorentz signature and twisted spectral triples
A. Devastato, S. Farnsworth, F. Lizzi, and P. Martinetti · 2018
Later among the works it cites.
Spectral Action in Noncommutative Geometry
M. Eckstein and B. Iochum · 2018
Later among the works it cites.
Clifford Structures in noncommutative geometry and the extended scalar sector
M.A. Kurkov and F. Lizzi · 2018
Later among the works it cites.
Gauge transformations for twisted spectral triples
G. Landi and P. Martinetti · 2018
Later among the works it cites.
Noncommutative Geometry and Particle Physics
F. Lizzi · 2018
Later among the works it cites.
Deducing the symmetry of the standard model from the automorphism and structure groups of the exceptional Jordan algebra
I. Todorov and M. Dubois-Violette · 2018
Later among the works it cites.