The quantum structure of spacetime at the Planck scale and quantum fields

Abstract

We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg's principle and by Einstein's theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation relations exactly implement our uncertainty relations. We outline the definition of free fields and interactions over QST and take the first steps to adapting the usual perturbation theory. The quantum nature of the underlying spacetime replaces a local interaction by a specific nonlocal effective interaction in the ordinary Minkowski space. A detailed study of interacting QFT and of the smoothing of ultraviolet divergences is deferred to a subsequent paper. In the classical limit where the Planck length goes to zero, our Quantum Spacetime reduces to the ordinary Minkowski space times a two component space whose components are homeomorphic to the tangent bundle TS^2 of the 2-sphere. The relations with Connes' theory of the standard model will be studied elsewhere.

TeX, 37 pages. Since recent and forthcoming articles (hep-th/0105251, hep-th/0201222, hep-th/0301100) are based on this paper, we thought it would be convenient for the readers to have it available on the web

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• Testing fundamental physics with photon frequency shift
• The ultraviolet infrared mixing problem on the noncommutative Moyal space
• Neutron-antineutron transition as a test-bed for dynamical CPT violations
• Canonical k-Minkowski Spacetime
• On algebraic supergroups, coadjoint orbits and their deformations
• Infrared cutoffs and the adiabatic limit in noncommutative spacetime
• Scattering in three-dimensional fuzzy space
• On the role of Schwinger's SU(2) generators for Simple Harmonic Oscillator in 2D Moyal plane
• The quantum clock: a critical discussion on space-time
• Entropy, temperature and internal energy of trapped gravitons and corrections to the Black Hole entropy
• Discrete Time Evolution and Energy Nonconservation in Noncommutative Physics
• On the Plethora of Representations Arising in Noncommutative Quantum Mechanics and An Explicit Construction of Noncommutative 4-tori
• $\mathcal{P}\mathcal{T}$-symmetric quantum field theory on the noncommutative spacetime
• Thermofield dynamics and twisted Poincaré symmetry on Moyal space-time
• Compact stars in quantum spacetime
• Finite-matrix formulation of gauge theories on a non-commutative torus with twisted boundary conditions
• The Noncommutative Doplicher-Fredenhagen-Roberts-Amorim Space
• Line element in quantum gravity: the examples of DSR and noncommutative geometry
• Quantum $D=3$ Euclidean and Poincaré symmetries from contraction limits
• Wedge-Local Quantum Fields on a Nonconstant Noncommutative Spacetime
• Extending general covariance: Moyal-type noncommutative manifolds
• Quantum clock: A critical discussion on spacetime
• Entropy, energy and temperature-length inequality for Friedmann universes
• Quantum Field Theory on quantized Bergman domain
• One-loop calculations in CPT-even Lorentz-breaking scalar QED
• Noncommutativity In The Mechanics Of A Free Massless Relativistic Particle
• On a physical description and origin of the cosmological constant
• Misleading inferences from discretization of empty spacetime: Snyder-noncommutativity case study
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• The Cutkosky rule of three dimensional noncommutative field theory in Lie algebraic noncommutative spacetime
• Exploring the thermodynamics of non-commutative scalar fields
• Violation of Lorentz invariance and dynamical effects in high energy gamma rays
• Exact solutions of a damped harmonic oscillator in a time dependent noncommutative space
• Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
• Events in a Non-Commutative Space-Time
• From UV/IR mixing to closed strings
• Non Local Theories: New Rules for Old Diagrams
• Locally Noncommutative Space-Times
• How not to establish the non-renormalizability of gravity
• On the Meaning of the String-Inspired Noncommutativity and its Implications
• Noncommutative Electrodynamics with covariant coordinates
• Noncommutativity and the Weak Cosmic Censorship
• MICZ Kepler Systems in Noncommutative Space and Duality of Force Laws
• q-Translations on quantum spaces
• Planckian corrections to the Friedmann flat equations from thermodynamics at the apparent horizon
• Coisotropic Lie bialgebras and complementary dual Poisson homogeneous spaces
• Generalized quantum phase spaces for the $\kappa$-deformed extended Snyder model
• Noncommutative phase-space effects in thermal diffusion of Gaussian states
• Exact solution of damped harmonic oscillator with a magnetic field in a time dependent noncommutative space
• Fingerprints of the quantum space-time in time-dependent quantum mechanics: An emergent geometric phase
• Building a linear equation of state for trapped gravitons from finite size effects and the Schwarzschild black hole case
• A brief remark on Unruh effect and causality
• Equivalence principle in context of large uniform acceleration - a quantum mechanical perspective
• Deformation of the quintom cosmological model and its consequences
• Violation of Remaining Lorentz Symmetry in the Approach of Time-Ordered Perturbation Theory to Space-Time Noncommutativity
• Non-commutative Geometry from Perturbative Quantum Gravity in de Sitter spacetime
• Spacetime-Free Approach to Quantum Theory and Effective Spacetime Structure
• Light incoherence due to quantum-gravitational fluctuations of the background space
• The Weyl realizations of Lie algebras and left-right duality
• Thermodynamics of high order correction for Schwarzschild-AdS black hole in non-commutative geometry
• On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
• Classical electrodynamics on Snyder space
• Space-time: Commutative or noncommutative ?
• External Fields as Intrinsic Geometry
• Covariance systems
• Hydrodynamics on non-commutative space --A step toward hydrodynamics of granular materials--
• Noncommutative magnetic moment, fundamental length and lepton size
• On UV/IR Mixing via Seiberg-Witten Map for Noncommutative QED
• Snyder Space-Time: K-Loop and Lie Triple System
• Noncommutative deformations of quantum field theories, locality, and causality
• On Poisson geometries related to noncommutative emergent gravity
• Dispersion relations in the noncommutative ϕ^3 and Wess-Zumino model in the Yang-Feldman formalism
• UV/IR mixing as a twisted Poincaré anomaly
• Generalized Non-Commutative Inflation
• And what if gravity is intrinsically quantic ?
• A Review of Noncommutative Field Theories
• Born--Oppenheimer decomposition for quantum fields on quantum spacetimes
• Why space could be quantised on a different scale to matter
• Non-Commutative Correction to Thin Shell Collapse in Reissner Nordstr$\ddot{o}$m Geometry
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• Bound state energies and phase shifts of a non-commutative well
• Dimensional flow in the kappa-deformed space-time
• Universal Enveloping Algebra and Differential Calculi on Orthogonal q-groups
• Magnetic Monopole in Noncommutative Space-Time and Wu-Yang Singularity-Free Gauge Transformations
• From Snyder space-times to doubly $\kappa$-dependent Yang quantum phase spaces and their generalizations
• Photonic realization of the kappa-deformed Dirac equation
• Quantum space and quantum completeness
• On the Quantum Space-Time Coordinates of an Event
• Generalized twist deformations of Poincare and Galilei Hopf algebras
• Classical dynamics on three dimensional fuzzy space: Connecting the short and long length scales
• Field Theory on a Non-commutative Plane: a Non-Perturbative Study
• Quantum field theories on noncommutative R^4 versus theta-expanded quantum field theories
• Quantum instability of gauge theories on $\kappa$-Minkowski space
• Low-Energy Lorentz Invariance in Lifshitz Nonlinear Sigma Models
• Wedge locality and asymptotic commutativity
• The entropy of dense non-commutative fermion gases
• Magnetic monopoles in noncommutative quantum mechanics
• Noncommutative quantum mechanics of simple matter systems interacting with circularly polarized gravitational waves
• Noncommutative of space-time and the relativistic Hydrogen atom
• Closedness of orbits in a space with SU(2) Poisson structure
• Analytical and numerical analysis of a rotational invariant D=2 harmonic oscillator in the light of different noncommutative phase-space configurations
• Two-photon annihilation of singlet cold dark matters due to noncommutative space-time
• Two roads to noncommutative causality
• Conjugate variables in quantum field theory: the basic case
• Aspects of perturbative quantum field theory on non-commutative spaces
• One loop radiative corrections to the translation-invariant noncommutative Yukawa Theory
• Two arguments for more fundamental building blocks
• Faddeev-Jackiw approach of the noncommutative spacetime Podolsky electromagnetic theory
• Gravitational probe of quantum spacetime
• Linear Connections on Fuzzy Manifolds
• Causal Fermion Systems and the ETH Approach to Quantum Theory
• Landau levels in a 2D noncommutative space: matrix and quaternionic vector coherent states
• Quantum Aspects of the Noncommutative Sine-Gordon Model
• Propagators and Matrix Basis on Noncommutative Minkowski Space
• Virtual Black Holes from Generalized Uncertainty Principle and Proton Decay
• Calculating the jet quenching parameter in the plasma of NCYM theory from gauge/gravity duality
• Phase space quantization, noncommutativity and the gravitational field
• A note on broken dilatation symmetry in planar noncommutative theory
• Twist for Snyder space
• On the consequences of twisted Poincare' symmetry upon QFT on Moyal noncommutative spaces
• Central tetrads and quantum spacetimes
• Information Theoretical Approach to Detecting Quantum Gravitational Corrections
• Thermodynamic phase transition and Joule-Thomson expansion of a quantum corrected black hole in AdS spacetime
• Twisted submanifolds of R^n
• Cornwall-Jackiw-Tomboulis effective potential for canonical noncommutative field theories
• Gravitational measurements in higher dimensions
• N-Particle Scattering in Relativistic Wedge-Local Quantum Field Theory
• ESA Voyage 2050 white paper -- GrailQuest: hunting for Atoms of Space and Time hidden in the wrinkle of Space-Time
• Complete solution of the LSZ Model via Topological Recursion
• Length and distance on a quantum space
• Extended noncommutative Minkowski spacetimes and hybrid gauge symmetries
• Statistical description of massless excitations within a sphere with a linear equation of state and the dark energy case
• Comment on "Can we measure structures to a precision better than the Planck length?"[arXiv:1205.3636], by Sabine Hossenfelder
• Star Product Geometries
• Particle Dynamics And Emergent Gravity
• Noncommutative Brownian motion
• Position Operators and Center of Mass: New Perspectives
• The cosmological constant from Planckian fluctuations and the averaging procedure
• Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time
• Symplectic Deformations, Non Commutative Scalar Fields and Fractional Quantum Hall Effect
• Matrix Field Theory
• Twisted Covariance and Weyl Quantisation
• Energy corrections due to the noncommutative phase-space of the charged isotropic harmonic oscillator in a uniform magnetic field in 3D
• Noncommutative (supersymmetric) electrodynamics in the Yang-Feldman formalism
• Holographic Bound in Quantum Field Energy Density and Cosmological Constant
• Noncommutative quasinormal modes of Schwarzschild black hole
• Learning a Deep Model for Human Action Recognition from Novel Viewpoints
• Preconjugate variables in quantum field theory and their use
• Noncommutative supersymmetric Chern-Simons-matter model
• Noncommutative Time in Quantum Field Theory
• Reply to "Comment on 'Noncommutative gauge theories and Lorentz symmetry'"
• Effects of wave propagation in canonical Poisson gauge theory under an external magnetic field
• Quantum Kaluza-Klein theory with $M_2(\mathbb{C})$
• Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
• Multi-particle systems in quantum spacetime and a novel challenge for center-of-mass motion
• Unitarity of noncommutative field theories from string theory
• Conformal quantum mechanics and holography in noncommutative space-time
• Noncommutative Vortices and Instantons from Generalized Bose Operators
• Emergence of maximal acceleration from non-commutativity of space-time
• Phase structure of fuzzy black holes
• On the Quantization of Length in Noncommutative Spaces
• The ultraviolet-finite Hamiltonian approach on the noncommutative Minkowski space
• UV Finite Field Theories on Noncommutative Spacetimes: the Quantum Wick Product and Time Independent Perturbation Theory
• Maximal acceleration in a Lorentz invariant non-commutative space-time
• TeV-photon paradox and space with SU(2) fuzziness
• Constraints on the scalar potential from spectral action principle
• Spectral distances on doubled Moyal plane using Dirac eigen-spinors
• Computing the spectral action for fuzzy geometries: from random noncommutative geometry to bi-tracial multimatrix models
• Quantized Kähler Geometry and Quantum Gravity
• Consistency of an alternative CPT-odd and Lorentz-violating extension of QED
• Quantization of the open string on plane-wave limits of dS_n x S^n and non-commutativity outside branes
• Poincaré Covariant k-Minkowski Spacetime
• Uniformly Accelerated Observer in Moyal Spacetime
• Spin and Statistics and First Principles
• Twist Deformations of the Supersymmetric Quantum Mechanics
• Notes on several phenomenological laws of quantum gravity
• Possible quantum kinematics. II. Non-minimal case
• Basic quantizations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries
• Linear hyperbolic PDEs with non-commutative time
• C*-Multipliers, crossed product algebras, and canonical commutation relations
• Quantum Entanglement of Fermions- Antifermions Pair Creation modes in Non-commutative Bianchi I Space-time
• Quantum Reference Frames and Quantum Transformations
• Trace of phase-space noncommutativity in the response of a free particle to linearized gravitational waves
• Localization at threshold in noncommutative space
• Deformation Quantization of Surjective Submersions and Principal Fibre Bundles
• Noncommutative field theories from a deformation point of view
• On Charge Conservation and The Equivalence Principle in the Noncommutative Spacetime
• Space-time noncommutativity with a bifermionic parameter
• Noncommutative Lagrange Mechanics
• One-loop unitarity of scalar field theories on Poincare invariant commutative nonassociative spacetimes
• Noncommutative Spherically Symmetric Spaces
• Thermodynamical features of Verlinde's approach for a non-commutative Schwarzschild-anti-deSitter black hole in a broad range of scales
• Novel Ambiguities in the Seiberg-Witten Map and the Emergent Gravity
• Conserved symmetries in noncommutative quantum mechanics
• The Hierarchy Problem: From the Fundamentals to the Frontiers
• Asymptotic commutativity of quantized spaces: the case of ${\mathbb{CP}}^{p,q}$
• A proposal for Heisenberg uncertainty principle and STUR for curved backgrounds: an application to white dwarf, neutron stars and black holes
• Poisson electrodynamics on $\kappa$-Minkowski space-time
• A Stochastic Origin of Spacetime Non-Commutativity
• Fermi acceleration under Lorentz invariance violation
• Newtonian cosmology and Evolution of kappa-deformed universe
• Fuzzy hyperspheres via confining potentials and energy cutoffs
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Quantum Riemannian geometry of the discrete interval and q-deformation
• Exact solutions for scalars and spinors on quantized (Euclidean) $Ad{S}_2$ and the correspondence principle
• Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra
• The physical origin of the cosmological constant: continuum limit and the analogy with the Casimir effect
• $U(N)$ Yang-Mills in non-commutative space time
• Two-particle system in Coulomb potential for twist-deformed space-time
• Non-Commutative space-time and Hausdorff dimension
• Revisiting Connes' Finite Spectral Distance on Non-commutative Spaces : Moyal Plane and Fuzzy Sphere
• Spontaneous symmetry breaking and masses numerical results in DFR noncommutative space-time
• Scalar fields in a non-commutative space
• Central force problem in space with SU(2) Poisson structure
• QED Representation for the Net of Causal Loops
• Covariant Fields of C*-Algebras under Rieffel Deformation
• Spectral dimension of Horava-Snyder spacetime and the $Ad{S}_2\times S^2$ momentum space
• Harmonic oscillator in twisted Moyal plane: eigenvalue problem and relevant properties
• Dominance of a single topological sector in gauge theory on non-commutative geometry
• Random versus holographic fluctuations of the background metric. I. (Cosmological) running of space-time dimension
• The instability of intersecting fuzzy spheres
• Interacting Relativistic Particle: Time-Space Noncommutativity And Symmetries
• Moduli spaces of discrete gravity I: A few points
• Duality of Coordinates and Matter Fields in Curved Spacetime
• Classical Gravity on Fuzzy Space-Time
• Beyond second-moment approximation in fuzzy-field-theory-like matrix models
• Light Propagation in $\kappa$-Minkowski Space-Time: Gauge Ambiguities and Invariance
• $\kappa$-deformed power spectrum and modified Unruh temperature
• Morita Equivalence, Picard Groupoids and Noncommutative Field Theories
• Regularization of Kepler Problem in $\kappa$-spacetime
• Noncommutativity and Duality through the Symplectic Embedding Formalism
• Covariant formulation of Noether's Theorem for translations on kappa-Minkowski spacetime
• A Deformation Quantization for Non-Flat Spacetimes and Applications to QFT
• Covariant dynamics on the energy-momentum space: scalar field theory
• The Strong Interaction Model in DFR noncommutative space-time
• Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries
• Twisting loops and global momentum non-conservation in Relative Locality
• Quantum groups and noncommutative spacetimes with cosmological constant
• Neutron Star in Quantized-space-time
• Yang-Mills field from fuzzy sphere quantum Kaluza-Klein model
• Noncommutative geometry of the Moyal plane: translation isometries, Connes' distance on coherent states, Pythagoras equality
• Estimating the strength of Lorentzian distribution in non-commutative geometry by solar system tests
• Quantum Klein Space and Superspace
• Towards new relativistic doubly $\kappa$-deformed D=4 quantum phase spaces
• Bicrossproduct construction versus Weyl-Heisenberg algebra
• Causality in Non-Commutative Quantum Field Theories
• Pinhole interference in three-dimensional fuzzy space
• Quantum field theory on a discrete space and noncommutative geometry
• Is life a thermal horizon ?
• An Arena for Model Building in the Cohen-Glashow Very Special Relativity
• kappa-Deformed Oscillators: Deformed Multiplication Versus Deformed Flip Operator and Multiparticle Clusters
• Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence
• Could the photon dispersion relation be non-linear ?
• Generalized Heisenberg algebra, realizations of the $\mathfrak{gl}(n)$ algebra and applications
• The deformed two-dimensional black hole
• Braided Field Quantization from Quantum Poincare Covariance
• Quantization of Spacetime Based on Spacetime Interval Operator
• Two approaches to quantum gravity and M-(atrix) theory at large number of dimensions
• Non-commutative coordinates from quantum gravity
• Strict deformations of quantum field theory in de Sitter spacetime
• A scale-covariant quantum space-time
• The physical nature of the cosmological constant and the decoherence scale in a renormalization-group approach
• Residual gauge-invariance in a massive Lorentz-violating extension of QED
• All-Loop Renormalizable Wess-Zumino Model on Bosonic-Fermionic Noncommutative Superspace
• Global Space-Time Symmetries of Quantized Euclidean and Minkowski Superspaces
• On localized and coherent states on some new fuzzy spheres
• Pair production of Dirac particles in a d+1-dimensional noncommutative space-time
• A Spectral Triple for a Solenoid Based on the Sierpinski Gasket
• Relativistic Corrections to the Moyal-Weyl Spacetime
• Noncommutative Geometry: Fuzzy Spaces, the Groenewold-Moyal Plane
• Pale Glares of Dark Matter in Quantum Spacetime
• Quantisation of Lorentz invariant scalar field theory in non-commutative space-time and its consequence
• Twisted Supersymmetry in a Deformed Wess-Zumino Model in (2+1) Dimensions
• Consistent Construction of Perturbation Theory on Noncommutative Spaces
• Quantum Cosmological Backreactions III: Deparametrised Quantum Cosmological Perturbation Theory
• Force in Kappa-Deformed Relativistic Dynamics
• Separation of noncommutative differential calculus on quantum Minkowski space
• Model of a quantum particle in spacetime
• Total momentum and other Noether charges for particles interacting in a quantum spacetime
• Covariance approach to the free photon field
• Wave Propagation and IR/UV Mixing in Noncommutative Spacetimes
• Dirac Operators on Noncommutative Curved Spacetimes
• Quantum harmonic oscillator in a time dependent noncommutative background
• T-Minkowski noncommutative spacetimes I: Poincaré groups, differential calculi and braiding
• Radiative corrections to the Chern-Simons term at finite temperature in the noncommutative Chern-Simons-Higgs model
• Generalized twist deformations of Poincare and Galilei quantum groups
• Projective module description of embedded noncommutative spaces
• Quantum-gravitational running/reduction of space-time dimension
• General Covariance in Algebraic Quantum Field Theory
• Some considerations on duality concerning kappa-Minkowski spacetime theories
• The coordinate coherent states approach revisited
• Ultraviolet-infrared mixing on the noncommutative Minkowski space in the Yang-Feldman formalism
• DFR Perturbative Quantum Field theory on Quantum Space Time, and Wick Reduction
• Braided Tensor Products and the Covariance of Quantum Noncommutative Free Fields
• Commutative deformations of general relativity: nonlocality, causality, and dark matter
• To the Memory of Alexander Grothendieck: a Great and Mysterious Genius of Mathematics
• Some Features of Scattering Problem in a $\kappa$-Deformed Minkowski Spacetime
• Curving Flat Space-Time by Deformation Quantization?
• Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics
• A brief introduction to the noncommutative geometry description of particle physics standard model
• Quantized Equations of Motion and Currents in Noncommutative Theories
• Spinor calculus for q-deformed quantum spaces II
• A Poincaré Covariant Noncommutative Spacetime?
• Search for the Footprints of New Physics with Laboratory and Cosmic Neutrinos
• Three Short Distance Structures from Quantum Algebras
• Energy momentum tensor for translation invariant renormalizable noncommutative field theory
• Deformations of the Canonical Commutation Relations and Metric Structures
• Generalization of Weyl realization to a class of Lie superalgebras
• Braided algebras and the kappa-deformed oscillators
• From quantum deformations of relativistic symmetries to modified kinematics and dynamics
• Quantum theory, noncommutative gravity, and the cosmological constant problem
• Supersymmetry breaking in noncommutative quantum mechanics
• The 1/N Expansion in Noncommutative Quantum Mechanics
• Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
• Time dependent transitions with time-space noncommutativity & its implications in Quantum Optics
• The Structure of Spacetime and Noncommutative Geometry
• A noncommutative geometric approach to the quantum structure of spacetime
• The DFR-Algebra for Poisson Vector Bundles
• The Majid-Ruegg model and the Planck scales
• Thermal effective potential in two- and three- dimensional non-commutative spaces
• Eigenvalue problem for radial potentials in space with SU(2) fuzziness
• One-Loop Renormalizable Wess-Zumino Model on Bosonic-Fermionic Noncommutative Superspace
• Green's Functions for Translation Invariant Star Products
• The standard electroweak model in the noncommutative $DFR$ space-time
• Conjugate variables in quantum field theory and a refinement of Paulis theorem
• Spherically symmetric potential in noncommutative spacetime with a compactified extra dimensions
• Deformation of Noncommutative Quantum Mechanics
• Retarded Functions in Noncommutative Theories
• Geometrical techniques for the N-dimensional Quantum Euclidean Spaces
• Einstein Equations for a Noncommutative Spacetime of Lie-Algebraic Type
• The $q$-linked complex Minkowski space, its real forms and deformed isometry groups
• Two ${\theta }_{\mu \nu }$ -deformed covariant relativistic quantum phase spaces as Poincare-Hopf algebroids
• Quantum Spacetime and the Universe at the Big Bang, vanishing interactions and fading degrees of freedom
• Yang-Mills action from minimally coupled bosons on R^4 and on the 4D Moyal plane
• A general relativity formulation for the Doplicher-Fredenhagen-Roberts noncommutative space-time
• Exploring the gravity sector of emergent higher-spin gravity: effective action and a solution
• Spinorial Snyder and Yang Models From Superalgebras And Noncommutative Quantum Superspaces
• Space-time noncommutativity and (1+1) Higgs Model
• Signatures of quantum geometry from exponential corrections to the black hole entropy
• Noncommutative $Ad{S}_2$ I: Exact solutions
• Effective Potential and Spontaneous Symmetry Breaking in the Noncommutative phi^6 Model
• On the UV/IR mixing of Lie algebra-type noncommutatitive ${\varphi }^4$-theories
• Twisting kappa-deformed phase space
• Noncommutative instantons on $d=2n$ planes from matrix models
• Non-commutative correction of ideal gas thermodynamics
• Entropy of black holes, charged probes and noncommutative generalization
• Entropic force and bouncing behaviour in $\kappa$-Minkowski space-time
• Horizon quantum geometries and decoherence
• Effects of quantum geometry on the decoherence induced by black holes
• Thermostatistical analysis and negative heat capacities of Yukawa and Lee-Wick potentials in noncommutative phase spaces
• Quantum speed limit as a sensitive probe of Planck-scale effects
• Yang model revisited
• Fuzzy field theories and related matrix models
• Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory. II
• Chiral Spin Noncommutative Space and Anomalous Dipole Moments
• Quantum Gravity models - brief conceptual summary
• A note on the implementation of Poincaré symmetry in noncommutative field theory
• The Slavnov-Taylor Identities for the 2+1 Dimensional Noncommutative CP${}^{N-1}$ Model
• Local Space-Time Curvature Effects on Quantum Orbital Angular Momentum
• Variance of the Quantum Coordinates of an Event
• Vulcanized Vortex
• q-Deformed Superalgebras
• Testing Lorentz Violation Using Propagating UHECRs
• On the Geometry of the Quantum Poincare Group
• Waves on Noncommutative Spacetimes
• Fuzzy Space-Time
• Study on Noncommutative Representations of Galilean Generators
• On Finite Noncommutativity in Quantum Field Theory
• Fermions Coupled to Emergent Noncommutative Gravity
• Random versus holographic fluctuations of the background metric. II. Note on the dark energies arising due to microstructure of space-time
• Quantum Space-Time and Noncommutative Gauge Field Theories
• On 2d gravity and parallel transport field equation on quantum sphere
• The 3D perturbed Schrödinger Hamiltonian in a Friedmann flat spacetime testing the primordial universe in a non commutative spacetime
• The G-wavefront set and the twisted convolution product
• Dynamic and static properties of Quantum Hall and Harmonic Oscillator systems on the non-commutative plane
• Comments on Noncommutative Field Theories
• Quantum kinematics on q-deformed quantum spaces II, Wave functions on position and momentum space
• On the Non-Flatness Nature of Noncommutative Minkowski Spacetime and the Singular Behavior of Probes
• Twisted geometry for submanifolds of ${\mathbb{R}}^n$
• Review of Twisted Poincare Symmetry
• Algebraic structures in $\kappa$-Poincaré invariant gauge theories
• Radiation Reaction in Non-commutative Electrodynamics
• Quantum kinematics on q-deformed quantum spaces I, Mathematical Framework
• Energy corrections due to the Non-commutative Phase-Space of the Charged Harmonic Oscillator in a constant magnetic field in 3D
• Noncommutative geometry and quantization
• Compactification, T-Duality and Quantum Erasers
• Lattice oscillator model on noncommutative space: eigenvalues problem for the perturbation theory
• The flux of noncommutative U(1) instanton through the fuzzy spheres
• A note on the fuzzy sphere area spectrum, black hole luminosity, and the quantum nature of spacetime
• A relation between deformed superspace and Lee-Wick higher-derivative theories
• Noncommutative $\mathcal{N}=2$ Chern-Simons-matter model
• A Twisted ${\mathcal{C}}^{\star }$-algebra formulation of Quantum Cosmology with application to the Bianchi I model
• Einstein's lifts and topologies: topological investigations on the Principle of Equivalence
• Electromagnetic Excitations of Hall Systems on Four Dimensional Space
• Theories on noncommutative spaces and deformed symmetries
• Non-relativistic Schroedinger theory on q-deformed quantum spaces III, Scattering theory
• Non-relativistic Schroedinger theory on q-deformed quantum spaces II, The free non-relativistic particle and its interactions
• The universality question for noncommutative quantum field theory
• N=1/2 Global SUSY: R-Matrix Approach
• Vacuum Pair Creation in Spin Noncommutative of Coordinates: Volkov Background and Constant Electric Field
• Noncommutative spaces with twisted symmetries and second quantization
• Quantum Spacetimes from General Relativity?
• Twist-Deformed Lorentzian Heisenberg-Algebras
• The Photon Dispersion as an Indicator for New Physics ?
• Unruh effect using Doppler shift method in DSR framework
• Deriving Ontological Statements from the Unnatural Higgs Mass
• Quantization of Length in Spaces with Position-Dependent Noncommutativity
• Corrections to the Black hole entropy from a Bose Einstein condensate: a semi-classical phenomenological approach
• Fubctional integral approach to quantum gauge theories on a noncommutative space-time
• A Quantum Energy Inequality for a Non-commutative QFT
• Wick rotation for quantum field theories on degenerate Moyal space(-time)
• Braided Statistics from Abelian Twist in $\kappa$-Minkowski Spacetime
• Propagation features of Lorentz-violating electrodynamics
• Realizations of the Extended Snyder Model
• Quantum Spacetime: Echoes of basho
• Statistical interparticle potential on noncommutative space
• On the nonlinear electrodynamics in a Lorentz-breaking scenario
• Statistical physics on Euclidean Snyder space: connections with the GUP and cosmological implications
• Quantum geometry from commutators: a Heisenberg-picture framework and a toy application to early structure
• Noncommutative scalar fields from symplectic deformation
• Formal GNS Construction and States in Deformation Quantization
• Noncommutativity in Configuration Space Induced by A Conjugate Magnetic Field in Phase Space
• Renormalization on the DFR Quantum Spacetime
• $\hslash$-perturbative solutions of quantum Snyder and Yang models with parameters describing spontaneous symmetry breaking
• General $O(D)$-equivariant fuzzy hyperspheres via confining potentials and energy cutoffs
• Aspects of noncommutativity in field theory, strings and membranes