Review of the Phenomenology of Noncommutative Geometry

Abstract

We present a pedagogical review of particle physics models that are based on the noncommutativity of space-time, $[{\hat{x}}_{\mu },{\hat{x}}_{\nu }]=i{\theta }_{\mu \nu }$, with specific attention to the phenomenology these models predict in particle experiments either in existence or under development. We summarize results obtained for high energy scattering such as would occur for example in a future $e^{+}{e}^{-}$ linear collider with $\sqrt{s}=500GeV$, as well as low energy experiments such as those pertaining to elementary electric dipole moments and other $\cpviolng$ observables, and finally comment on the status of phenomenological work in cosmology and extra dimensions.

updated, references added, corrected typos

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• Observational Limits on Quantum Geometry Effects
• The photon-neutrino interaction in non-commutative gauge field theory and astrophysical bounds
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• Space-Time Noncommutativity, Discreteness of Time and Unitarity
• A Note on Superfields and Noncommutative Geometry
• Renormalization of noncommutative U(N) gauge theories
• The Meaning of Infrared Singularities in Noncommutative Gauge Theories
• Lepton anomalous magnetic moments - a theory update
• Superluminal Noncommutative Photons
• Signals for Non-Commutative QED in $e\gamma$ and $\gamma \gamma$ Collisions
• Signals for Non-Commutative QED in $e\gamma$ and $\gamma \gamma$ Collisions
• Non-Commutativity and Unitarity Violation in Gauge Boson Scattering
• Pair Production of Neutral Higgs Bosons through Noncommutative QED Interactions at Linear Colliders
• Noncommutative Quantum Field Theories
• CP violation from noncommutative geometry
• Compton scattering in Noncommutative Space-Time at the NLC
• Signatures of Non-commutative QED at Photon Colliders
• On the IR/UV mixing and experimental limits on the parameters of canonical noncommutative spacetimes
• Probing Noncommutative Space-Time in the Laboratory Frame
• Non-commutative geometry as a realization of varying speed of light cosmology
• Noncommutative Synchrotron
• Anomalous C-violating Three Photon Decay of the Neutral Pion in Noncommutative Quantum Electrodynamics
• Triple Neutral Gauge Boson Couplings in Noncommutative Standard Model
• Signals for Noncommutative QED at Future $e^{+}{e}^{-}$ Colliders
• Discerning Noncommutative Extra Dimensions
• Positronium Hyperfine Splitting in Non-commutative Space at the Order ${\alpha }^6$
• Have we already detected astrophysical symptoms of space-time noncommutativity ?
• Non-commutative space-time and the uncertainty principle
• Noncommutative renormalization for massless QED
• Noncommutative QED and Muon Anomalous Magnetic Moment
• Shadow of noncommutativity
• Noncommutative QED and the Lifetimes of Ortho and Para Positronium
• Noncommuting Coordinates in the Landau Problem
• The inclusive b -> s γdecay in the noncommutative standard model
• Phenomenological Consequences of Non-commutative QED
• Possible Effects of Noncommutative Geometry on Weak CP Violation and Unitarity Triangles
• The (gamma gamma -> H^0 H^0) process in noncommutative quantum electrodynamics
• Signals for Noncommutative QED at High Energy $e^{+}{e}^{-}$ Colliders
• An Introduction to Noncommutative Geometry
• Theoretical Status of Muon (g-2)
• Phenomenology of Non-Commutative Field Theories
• Theoretical status of the muon g-2
• The one-loop QED in Noncommutative space
• Atomic Probes of Noncommutative Field Theory
• Scattering Cross Sections and Lorentz Violation

Cited by in corpus (116)

• Quantum Field Theory on Noncommutative Spaces
• Modern tests of Lorentz invariance
• Minimal Length Scale Scenarios for Quantum Gravity
• Noncommutative Black Holes, The Final Appeal To Quantum Gravity: A Review
• Preferred-Frame and CP-Violation Tests with Polarized Electrons
• Non-Commutative GUTs, Standard Model and C,P,T
• Searches for the role of spin and polarization in gravity
• Parikh-Wilczek Tunneling from Noncommutative Higher Dimensional Black Holes
• Noncommutative Gauge Theory without Lorentz Violation
• Noncommutative quantum mechanics and the Aharonov-Casher effect
• Probing the Noncommutative Standard Model at Hadron Colliders
• Dimensional Reduction over Fuzzy Coset Spaces
• Hawking radiation as tunneling from a Vaidya black hole in noncommutative gravity
• K -> pi gamma decays and space-time noncommutativity
• Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere
• Magnetic Backgrounds and Noncommutative Field Theory
• Noncommutative Dirac oscillator in an external magnetic field
• Quarkonia decays into two photons induced by the space-time non-commutativity
• Generalized uncertainty principle or curved momentum space?
• Effective Field Theories on Non-Commutative Space-Time
• Aharonov-Bohm effect in a Class of Noncommutative Theories
• Phenomenology of Lorentz-Conserving Noncommutative QED
• Black Hole Remnants in Hayward Solutions and Noncommutative Effects
• Unusual High-Energy Phenomenology of Lorentz-Invariant Noncommutative Field Theories
• Entropic force approach to noncommutative Schwarzschild black holes signals a failure of current physical ideas
• On the IR/UV mixing and experimental limits on the parameters of canonical noncommutative spacetimes
• Yukawa couplings and seesaw neutrino masses in noncommutative gauge theory
• Search for Lorentz and CPT violation using sidereal time dependence of neutrino flavor transitions over a short baseline
• Aharonov-Casher effect for spin one particles in a noncommutative space
• Photon-neutrino interaction in theta-exact covariant noncommutative field theory
• Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
• Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space
• The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios
• On Time-Space Noncommutativity for Transition Processes and Noncommutative Symmetries
• Minimal Scales from an Extended Hilbert Space
• Lorentz-Invariant Non-Commutative QED
• Can noncommutative effects account for the present speed up of the cosmic expansion?
• On the Radiatively Induced Lorentz and CPT Violating Chern-Simons Term
• Four-dimensional Gravity on a Covariant Noncommutative Space
• Graphene and non-Abelian quantization
• Lagrangian Formulation of a Magnetostatic Field in the Presence of a Minimal Length Scale Based on the Kempf Algebra
• First Search for Exotic Z Boson Decays into Photons and Neutral Pions in Hadron Collisions
• Non-singular Brans-Dicke collapse in deformed phase space
• Bounds on the Parameter of Noncommutativity from Supernova SN1987A
• Möller and Bhabha scattering in the noncommutative standard model
• Entropic force approach in a noncommutative charged black hole and the equivalence principle
• Electron dynamics in noncommutative geometry with magnetic field and Zitterbewegung phenomenon
• Light-by-Light Scattering and Spacetime Noncommutativity
• Drell-Yan as an avenue to test noncommutative Standard Model at the Large Hadron Collider
• Lorentz Violation in the Higgs Sector and Noncommutative Standard Model
• Field Theory in Noncommutative Minkowski Superspace
• Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere
• Non-commutative Supersymmetric Quantum Mechanics
• Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes
• Four-Dimensional Gravity on a Covariant Noncommutative Space (II)
• Singlet particles as cold dark matter in noncommutative space-time
• The Noncommutative Standard Model and Polarization in Charged Gauge Boson Production at the LHC
• Noncommutativity in (2+1)-dimensions and the Lorentz group
• Constraints on Non-Commutative Physics Scale with Neutrino-Electron Scattering
• Seiberg-Witten map Invariant Scatterings
• Noncommutative Thermofield Dynamics
• Spontaneous breaking of translational invariance in non-commutative lambda phi^4 theory in two dimensions
• Noncommutative electrodynamics and ultra high energy gamma rays
• Causal sets and conservation laws in tests of Lorentz symmetry
• Noncommutativity from spectral flow
• Noncommutative Quantization for Noncommutative Field Theory
• Relativistic and nonrelativistic Landau levels for the noncommutative quantum Hall effect with anomalous magnetic moment in a conical Gödel-type spacetime
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Spacetime Deformation Effect on the Early Universe and the PTOLEMY Experiment
• Cancellation of soft and collinear divergences in noncommutative QED
• Exploring the thermodynamics of non-commutative scalar fields
• Noncommutative Maxwell-Chern-Simons theory (I): One-loop dispersion relation analysis
• Two-Point Functions on Deformed Spacetime
• Elimination of IR/UV via Gravity in Noncommutative Field Theory
• Planck-scale nonthermal correlations in a noncommutative geometry inspired Vaidya black hole
• Inferring the covariant $\Theta$-exact noncommutative coupling in the top quark pair production at linear colliders
• Space-time: Commutative or noncommutative ?
• Noncommutative Universe and Chameleon Field Dynamics
• Noncommutativity and Lorentz Violation in Relativistic Heavy Ion Collisions
• Noncommutative geometry induced by spin effects
• Photonic realization of the kappa-deformed Dirac equation
• Inhomogeneous chiral symmetry breaking in noncommutative four fermion interactions
• Noncommutative QED+QCD and $\beta$-function for QED
• A comparison of remnants in noncommutative Bardeen black holes
• Search for associated production of Higgs with Z boson in the noncommutative Standard Model at linear colliders
• A Field Theoretical Model in Noncommutative Minkowski Superspace
• Effect of earth rotation on pair production of Standard Model Higgs bosons at linear colliders in the noncommutative space-time
• Collider Tests of the Non-Commutative Standard Model
• TeV-photon paradox and space with SU(2) fuzziness
• Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions
• Laboratory frame analysis of $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ scattering in the Noncommutative Standard Model
• Influence of Gravity on noncommutative Dirac equation
• Loop Quantum Cosmology with a noncommutative quantum deformed photon gas
• Thermodynamical features of Verlinde's approach for a non-commutative Schwarzschild-anti-deSitter black hole in a broad range of scales
• Gravitational energy of a noncommutative Vaidya black hole
• Thin-shell gravastar in a noncommutative BTZ geometry
• Nonlocal regularisation of noncommutative field theories
• Spacetime Noncommutativity in Models with Warped Extradimensions
• One-loop $\beta$ function of noncommutative scalar $QE{D}_4$
• Wave Propagation and IR/UV Mixing in Noncommutative Spacetimes
• Can a Nonsymmetric Metric mimic NCQFT in $e^{+}{e}^{-}\to \gamma \gamma$ ?
• Nonsymmetric Gravity and Noncommutative Signals
• Observation of Ultra Fine Structures in Energy Levels of Prolate Nuclei
• Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes
• Perturbative Symmetries on Noncommutative Spaces
• Dynamics determines geometry
• Implications of Seiberg-Witten map on type-I superconductors
• Zitterbewegung in Noncommutative Geometry
• Waves on Noncommutative Spacetimes
• Testing Lorentz Violation Using Propagating UHECRs
• Electromagnetic Dualities on Noncommutative Space-Time and Symplectic Formalisms
• Energy Cost of Localization of Relational Quantum Information
• Noncommutative Jackiw-Pi model: One-loop renormalization
• On 2d gravity and parallel transport field equation on quantum sphere
• ${\pi }^{+}{\pi }^{+}$ and ${\pi }^{+}{\pi }^{-}$ colliding in noncommutative space
• Test of Space-Time Non-Commutativity at the Future Circular Collider