Spectral Noncommutative Geometry, Standard Model and all that

Abstract

We review the approach to the standard model of particle interactions based on spectral noncommutative geometry. The paper is (nearly) self-contained and presents both the mathematical and phenomenological aspects. In particular the bosonic spectral action and the fermionic action are discussed in detail, and how they lead to phenomenology. We also discuss the Euclidean vs. Lorentz issues and how to go beyond the standard model in this framework.

Section 8 rewritten. Review article to appear on the Intenartional Journal of Modern Physics A

References in corpus (86)

• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Noncommutative Perturbative Dynamics
• Heat kernel expansion: user's manual
• Gravity coupled with matter and foundation of non-commutative geometry
• The Spectral Action Principle
• Gravity and the standard model with neutrino mixing
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Making the Case for Conformal Gravity
• Sakharov's induced gravity: a modern perspective
• A Lorentzian version of the non-commutative geometry of the standard model of particle physics
• The Minimal Scale Invariant Extension of the Standard Model
• Why the Standard Model
• A non Supersymmetric SO(10) Grand Unified Model for All the Physics below $M_{GUT}$
• Resilience of the Spectral Standard Model
• Solution to the ghost problem in fourth order derivative theories
• Fermion Hilbert Space and Fermion Doubling in the Noncommutative Geometry Approach to Gauge Theories
• Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model
• Exceptional quantum geometry and particle physics
• The standard model in noncommutative geometry and fermion doubling
• Almost-Commutative Geometries Beyond the Standard Model
• Inflation in a scale invariant universe
• An algebraic formulation of causality for noncommutative geometry
• Non-equilibrium Chiral Magnetic/Vortical Effects in Viscous Fluids
• Natural inflation mechanism in asymptotic noncommutative geometry
• Grand Symmetry, Spectral Action, and the Higgs mass
• Grand Unification in the Spectral Pati-Salam Model
• Gravitational parity anomaly with and without boundaries
• Rethinking Connes' approach to the standard model of particle physics via non-commutative geometry
• Local covariant quantum field theory over spectral geometries
• Lorentz signature and twisted spectral triples
• New Scalar Fields in Noncommutative Geometry
• Non-Commutative Geometry, Non-Associative Geometry and the Standard Model of Particle Physics
• High energy bosons do not propagate
• Parity anomaly in four dimensions
• Higgs mass in Noncommutative Geometry
• Higgs Mass and Noncommutative Geometry
• Can (noncommutative) geometry accommodate leptoquarks?
• The Standard Model in noncommutative geometry: fundamental fermions as internal forms
• Ab Initio Study of 40Ca with an Importance Truncated No-Core Shell Model
• A superfluid helium converter for accumulation and extraction of ultracold neutrons
• Quantum Gravity Boundary Terms from Spectral Action of Noncommutative Space
• Dynamic critical behavior of the worm algorithm for the Ising model
• First observation of KL -> pi+- e-+ nu e+ e-
• Krein spectral triples and the fermionic action
• Spectral action beyond the weak-field approximation
• Wick Rotation and Fermion Doubling in Noncommutative Geometry
• Temporal Lorentzian Spectral Triples
• Product of real spectral triples
• Bosonic Spectral Action Induced from Anomaly Cancelation
• Renormalization of the asymptotically expanded Yang-Mills spectral action
• $B$-decay anomalies and scalar leptoquarks in unified Pati-Salam models from noncommutative geometry
• Pati-Salam Unification from Non-commutative Geometry and the TeV-scale $W_R$ boson
• The Higgs Mass, Superconnections and the TeV-scale Left-Right Symmetric Model
• Equations of Motion as Constraints: Superselection Rules, Ward Identities
• Scale-invariant inflation with one-loop quantum corrections
• Constraints on Unified Gauge Theories from Noncommutative Geometry
• Almost-Commutative Geometries Beyond the Standard Model II: New Colours
• Spectral action, Weyl anomaly and the Higgs-Dilaton potential
• Gauge transformations for twisted spectral triples
• Spectral action with zeta function regularization
• Spectral Regularisation: Induced Gravity and the Onset of Inflation
• The Standard Model in Noncommutative Geometry and Morita equivalence
• Non-commutative Geometry Beyond the Standard Model
• Almost-Commutative Geometries Beyond the Standard Model III: Vector Doublets
• Spectral action for torsion with and without boundaries
• Finite Pseudo-Riemannian Spectral Triples and The Standard Model
• Spectral action and neutrino mass
• The Higgs Mass and the Emergence of New Physics
• Forces from Connes' geometry
• The Gribov problem in Noncommutative QED
• Noncommutative Geometric Spaces with Boundary: Spectral Action
• Emergent spontaneous symmetry breaking and emergent symmetry restoration in rippling gravitational background
• Indefinite Kasparov modules and pseudo-Riemannian manifolds
• The 750 GeV diphoton excess in unified $SU(2{)}_L\times SU(2{)}_R\times SU(4)$ models from noncommutative geometry
• The graded product of real spectral triples
• Scalar field vacuum expectation value induced by gravitational wave background
• Differential calculus on Jordan algebra and Jordan modules
• Higgs-Dilaton Lagrangian from Spectral Regularization
• Global and local aspects of spectral actions
• Fermion masses, mass-mixing and the almost commutative geometry of the Standard Model
• Inhomogeneous modes in the PT-symmetric quantum cosmology
• Clifford Structures in Noncommutative Geometry and the Extended Scalar Sector
• Entangled Scent of a Charge
• The Gribov problem in Noncommutative gauge theory
• Scattering in pseudo-Hermitian quantum field theory and causality violation
• Clifford-based spectral action and renormalization group analysis of the gauge couplings

Cited by in corpus (10)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• On de Sitter Spacetime and String Theory
• On stability of Friedmann-Lemaître-Robertson-Walker solutions in doubled geometries
• Tolerance Relations and Quantization
• Spectral Distance on Lorentzian Moyal Plane
• Hamiltonian analysis in Lie-Poisson gauge theory
• Deformed Kac-Moody Algebra and Noncommutative Fermi Theory in Two-Dimensions
• Quantum Spacetime: Echoes of basho
• Spectral triple with real structure on fuzzy sphere
• Remark on the synergy between the heat kernel techniques and the parity anomaly