Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry

Abstract

We show that the $\kappa$-deformed Poincaré quantum algebra proposed for elementary particle physics has the structure of a Hopf agebra bicrossproduct $U(so(1,3))\cobicross T$. The algebra is a semidirect product of the classical Lorentz group $so(1,3)$ acting in a deformed way on the momentum sector $T$. The novel feature is that the coalgebra is also semidirect, with a backreaction of the momentum sector on the Lorentz rotations. Using this, we show that the $\kappa$-Poincaré acts covariantly on a $\kappa$-Minkowski space, which we introduce. It turns out necessarily to be deformed and non-commutative. We also connect this algebra with a previous approach to Planck scale physics.

12 pages. Revision: minor typos corrected

References in corpus (3)

• The Quantum Deformed Dirac Equation from the k-Poincare` Algebra
• The Dirac-Coulomb Problem for the $\kappa$-Poincare Quantum Group
• The quantum 2-dimensional Poincare group from quantum group contraction

Cited by in corpus (569)

• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Testable scenario for Relativity with minimum-length
• Minimal Length Scale Scenarios for Quantum Gravity
• Quantum Spacetime Phenomenology
• The principle of relative locality
• Planck-scale deformation of Lorentz symmetry as a solution to the UHECR and the TeV-$\gamma$ paradoxes
• Doubly-Special Relativity: First Results and Key Open Problems
• Doubly Special Relativity theories as different bases of $\kappa$--Poincaré algebra
• Planck-scale modified dispersion relations and Finsler geometry
• Generalized Uncertainty Principle: Approaches and Applications
• Introduction to Doubly Special Relativity
• Non-commutative space-time of Doubly Special Relativity theories
• Deformed Boost Transformations That Saturate at the Planck Scale
• Quantum symmetry, the cosmological constant and Planck scale phenomenology
• Observer-independent quanta of mass and length
• Dirac oscillator with nonzero minimal uncertainty in position
• Review on Generalized Uncertainty Principle
• Fractal properties of quantum spacetime
• Prospects for constraining quantum gravity dispersion with near term observations
• Coproduct and star product in field theories on Lie-algebra non-commutative space-times
• De Sitter space as an arena for Doubly Special Relativity
• Deformed Field Theory on kappa-spacetime
• Kappa-Minkowski space-time and the star product realizations
• Doubly Special Relativity and de Sitter space
• New realizations of Lie algebra kappa-deformed Euclidean space
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• Local D=4 Field Theory on $\kappa$--Deformed Minkowski Space
• 2+1 gravity and Doubly Special Relativity
• Interpretation of Quantum Field Theories with a Minimal Length Scale
• Geometry and field theory in multi-fractional spacetime
• Self-consistency in Theories with a Minimal Length
• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• Lorentz-covariant deformed algebra with minimal length and application to the 1+1-dimensional Dirac oscillator
• The Search for Quantum Gravity Signals
• Triply Special Relativity
• Improved limit on quantum-spacetime modifications of Lorentz symmetry from observations of gamma-ray blazars
• Conservation Laws in Doubly Special Relativity
• Covariant realizations of kappa-deformed space
• Phenomenology of Doubly Special Relativity
• Waves on Noncommutative Spacetime and Gamma-Ray Bursts
• Topics in Noncommutative Geometry Inspired Physics
• Quantum-Gravity Phenomenology: Status and Prospects
• Fock space, quantum fields and kappa-Poincaré symmetries
• Noncommutative Differential Calculus on the Kappa-Minkowski Space
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• Gravity-wave interferometers as probes of a low-energy effective quantum gravity
• Gauge theories on the kappa-Minkowski spacetime
• Quantum Groups and Noncommutative Geometry
• The Big-Bang Singularity in the framework of a Generalized Uncertainty Principle
• From noncommutative kappa-Minkowski to Minkowski space-time
• Hamilton geometry: Phase space geometry from modified dispersion relations
• Generalised Chern-Simons actions for 3d gravity and kappa-Poincare symmetry
• Realization of DSR-relativistic symmetries in Finsler geometries
• Hopf-algebra description of noncommutative-spacetime symmetries
• Testing Dispersion Relations of Quantum $\kappa$-Poincaré Algebra on Cosmological Ground
• Relative-locality distant observers and the phenomenology of momentum-space geometry
• Shadow of a Charged Rotating Non-Commutative Black Hole
• 4d Deformed Special Relativity from Group Field Theories
• Space-time quantum solves three experimental paradoxes
• Planck-scale-modified dispersion relations in FRW spacetime
• Enlarged Bound on the Measurability of Distances and Quantum $\kappa$-Poincarè Group
• Cosmic rays and TeV photons as probes of quantum properties of space-time
• A Lagrangian for DSR Particle and the Role of Noncommutativity
• Construction of $\theta$-Poincaré Algebras and their Invariants on ${\mathcal{M}}_{\theta }$
• Classical basis for kappa-Poincare algebra and doubly special relativity theories
• Diffusion on $\kappa$-Minkowski space
• On $\kappa$-Deformation and UV/IR Mixing
• Challenge to Macroscopic Probes of Quantum Spacetime Based on Noncommutative Geometry
• Speed of particles and a relativity of locality in $\kappa$-Minkowski quantum spacetime
• Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
• Expanding universe as a classical solution in the Lorentzian matrix model for nonperturbative superstring theory
• Generalized Quantum Relativistic Kinematics: a Stability Point of View
• Generalized Weyl systems and kappa-Minkowski space
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• The Free Particle in Deformed Special Relativity
• Constraints on the quantum gravity scale from kappa - Minkowski spacetime
• Fractional and noncommutative spacetimes
• Hermitian Analyticity, IR/UV Mixing and Unitarity of Noncommutative Field Theories
• Velocity of particles in Doubly Special Relativity
• Spontaneous Violation of Lorentz Invariance and Ultra-High Energy Cosmic Rays
• Dirac spinors for Doubly Special Relativity and $\kappa$-Minkowski noncommutative spacetime
• Relativistic deformed kinematics from momentum space geometry
• Gravity induced from quantum spacetime
• Local Field Theory ON $\kappa$-Minkowski Space, Star Products and Noncommutative Translations
• Generalized Poincare algebras, Hopf algebras and kappa-Minkowski spacetime
• Generalized kappa-deformed spaces, star-products, and their realizations
• Effects of quantum deformation on the spin-1/2 Aharonov-Bohm problem
• On the fate of Lorentz symmetry in relative-locality momentum spaces
• Symplectic geometry and Noether charges for Hopf algebra space-time symmetries
• Phenomenology of Particle Production and Propagation in String-Motivated Canonical Noncommutative Spacetime
• Spacetime-noncommutativity regime of Loop Quantum Gravity
• A glimpse at the flat-spacetime limit of quantum gravity using the Bekenstein argument in reverse
• Quantum deformations of the flat space superstring
• On the $\kappa$-Dirac Oscillator revisited
• Construction of Gauge Theories on Curved Noncommutative Spacetime
• Scalar field theory on $\kappa$-Minkowski space-time and Doubly Special Relativity
• Lorentz invariant field theory on kappa-Minkowski space
• Scalar field propagation in the phi^4 kappa-Minkowski model
• Symmetries of quantum space-time in 3 dimensions
• Derivatives, forms and vector fields on the kappa-deformed Euclidean space
• A no-pure-boost uncertainty principle from spacetime noncommutativity
• Noncommutative Spaces and Poincaré Symmetry
• Anomalous dimension in semiclassical gravity
• Anatomy of a deformed symmetry: field quantization on curved momentum space
• A non-commutative Minkowskian spacetime from a quantum AdS algebra
• Curved spacetimes with local $\kappa$-Poincaré dispersion relation
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Living in Curved Momentum Space
• Quantum reference frames and deformed symmetries
• Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes
• The UV/IR Interplay in Theories with Space-time Varying Non-commutativity
• Effective Field Theories on Non-Commutative Space-Time
• Noncommutative Model with Spontaneous Time Generation and Planckian bound
• Reaching the Planck scale with muon lifetime measurements
• κ-deformations of D=4 Weyl and conformal symmetries
• Landau Levels in the Presence of a Cosmic String in Rainbow Gravity
• Deformed relativity symmetries and the local structure of spacetime
• Kinematical solution of the UHE-cosmic-ray puzzle without a preferred class of inertial observers
• Physics of Deformed Special Relativity
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Classical paradoxes of locality and their possible quantum resolutions in deformed special relativity
• $\kappa$--deformed Wigner construction of relativistic wave functions and free fields on $\kappa$-Minkowski space
• Noncommutative Differential Forms on the kappa-deformed Space
• Classification of Differential Calculi on U_q(b+), Classical Limits, and Duality
• Rainbow statistics
• Newton's Equation on the kappa space-time and the Kepler problem
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Doubly special quantum and statistical mechanics from quantum $\kappa$-Poincaré algebra
• Localization and Reference Frames in $\kappa$-Minkowski Spacetime
• Quantization by cochain twists and nonassociative differentials
• Noncommutative scalar quasinormal modes and quantization of entropy of a BTZ black hole
• On the IR/UV mixing and experimental limits on the parameters of canonical noncommutative spacetimes
• Quantum fields, non-locality and quantum group symmetries
• Phenomenological consequences of a geometry in the cotangent bundle
• $\kappa$-deformed Dirac Equation
• Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime
• Differential structure on kappa-Minkowski space, and kappa-Poincare algebra
• Three-dimensional gravity and Drinfel'd doubles: spacetimes and symmetries from quantum deformations
• The kappa-(A)dS quantum algebra in (3+1) dimensions
• The $\kappa$-(A)dS noncommutative spacetime
• On kappa-deformation and triangular quasibialgebra structure
• Deformed relativistic kinematics on curved spacetime -- a geometric approach
• Noncommutative duality and fermionic quasinormal modes of the BTZ black hole
• $\kappa$-Poincaré invariant quantum field theories with KMS weight
• Doubly Special Relativity in Position Space Starting from the Conformal Group
• Distance Measurement and $\kappa$-Deformed Propagation of Light and Heavy Probes
• The Hidden Quantum Groups Symmetry of Super-renormalizable Gravity
• Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Group velocity in noncommutative spacetime
• kappa-Minkowski representations on Hilbert spaces
• Toward the classification of differential calculi on $\kappa$-Minkowski space and related field theories
• Doubly special relativity and translation invariance
• Gauge theories on quantum spaces
• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Observables and Dispersion Relations in k-Minkowski Spacetime
• Interplay between curvature and Planck-scale effects in astrophysics and cosmology
• Spectral noncommutative geometry and quantization: a simple example
• Quantum Deformations of Conformal Algebras Introducing Fundamental Mass Parameters
• Doubly Special Relativity: facts and prospects
• Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
• Maxwell's equations on the $\kappa$-Minkowski spacetime and Electric-Magnetic duality
• Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space
• Ground State of the Hydrogen Atom via Dirac Equation in a Minimal Length Scenario
• Differential algebras on kappa-Minkowski space and action of the Lorentz algebra
• Deformed Special Relativity in Position Space
• Curved momentum spaces from quantum (Anti-)de Sitter groups in (3+1) dimensions
• Planck-scale phenomenology with anti-de Sitter momentum space
• Unified description for kappa-deformations of orthogonal groups
• Quantum gravity on a square graph
• Relativistic and Newtonian kappa spacetimes
• Relativistic Thermodynamics with an Invariant Energy Scale
• Electrodynamics of a Generalized Charged Particle in Doubly Special Relativity Framework
• Noncommutative Geometries and Gravity
• DSR Relativistic Particle in a Lagrangian formulation and Non-Commutative Spacetime: A Gauge Independent Analysis
• Differential structure on the $\kappa$-Minkowski spacetime from twist
• The DSR-deformed relativistic symmetries and the relative locality of 3D quantum gravity
• Differential Structure on kappa-Minkowski Spacetime Realized as Module of Twisted Weyl Algebra
• Relative locality in a quantum spacetime and the pregeometry of $\kappa$-Minkowski
• Modeling transverse relative locality
• Planck-scale relativity from quantum $\kappa$-Poincaré algebra
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• Deformed and extended Galilei group Hopf algebras
• Introduction to Quantum-Gravity Phenomenology
• Towards the map of quantum gravity
• A symmetry invariant integral on kappa-deformed spacetime
• Phase spaces of Doubly Special Relativity
• The $\kappa$-Newtonian and $\kappa$-Carrollian algebras and their noncommutative spacetimes
• Noncommutative fields and the short-scale structure of spacetime
• Dual redshift on Planck-scale-curved momentum spaces
• Kappa-deformed oscillators, the choice of star product and free kappa-deformed quantum fields
• $\kappa$-Poincaré invariant orientable field theories at 1-loop
• Quantum Walks, Weyl equation and the Lorentz group
• Drinfel'd doubles for (2+1)-gravity
• Canonical and Lie-algebraic twist deformations of Galilei algebra
• A modular spectral triple for $\kappa$-Minkowski space
• $\kappa$-deformed complex fields and discrete symmetries
• Non-commutative relativistic spacetimes and worldlines from 2+1 quantum (anti-)de Sitter groups
• Gauge theories on $\kappa$-Minkowski spaces: Twist and modular operators
• Differential calculi on quantum Minkowski space
• Implications of Spacetime Quantization for the Bahcall-Waxman Neutrino Bound
• Almost commutative Riemannian geometry: wave operators
• On quantum deformations of (anti-)de Sitter algebras in (2+1) dimensions
• Have we already detected astrophysical symptoms of space-time noncommutativity ?
• Kinematics of particles with quantum de Sitter symmetries
• Deformed discrete symmetries
• Quantum Riemannian geometry and particle creation on the integer line
• The Momentum Spaces of $\kappa$-Minkowski noncommutative spacetime
• Doubly-Special Relativity: Facts, Myths and Some Key Open Issues
• Classical Mechanics on Noncommutative Space with Lie-algebraic Structure
• Uniformly accelerating observer in $\kappa$-deformed space-time
• A (2+1) non-commutative Drinfel'd double spacetime with cosmological constant
• The 2D $\kappa$-Dirac oscillator
• Beyond Special Relativity at second order
• Spectral geometry of $\kappa$-Minkowski space
• Berry Phase Effects in the dynamics of Dirac Electrons in Doubly Special Relativity Framework
• Geometric interpretation of Planck-scale-deformed co-products
• On the physical contents of q-deformed Minkowski spaces
• Noncommutative spaces of worldlines
• Quantum deformation of quantum cosmology: A framework to discuss the cosmological constant problem
• Braided Weyl algebras and differential calculus on U(u(2))
• Doubly Special Relativity as a Limit of Gravity
• Time Discretization From Noncommutativity
• Gauge Theories on Deformed Spaces
• Comparison of relativity theories with observer-independent scales of both velocity and length/mass
• $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
• Jordanian Quantum Deformations of D=4 Anti-de-Sitter and Poincare Superalgebras
• Kinematics of a relativistic particle with de Sitter momentum space
• Star product and interacting fields on $\kappa$-Minkowski space
• Entanglement dynamics in $\kappa$-deformed spacetime
• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• Signal propagation on $\kappa$-Minkowski spacetime and non-local two-point functions
• A bound on Planck-scale deformations of CPT from muon lifetime
• Weyl, Dirac and Maxwell Quantum Cellular Automata: analitical solutions and phenomenological predictions of the Quantum Cellular Automata Theory of Free Fields
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Light Cone in a Quantum Spacetime
• Deformed symmetries in noncommutative and multifractional spacetimes
• On the UV dimensions of Loop Quantum Gravity
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Laboratory bounds on Lorentz symmetry violation in low energy neutrino physics
• Curved momentum space, locality, and generalized space-time
• Planck-scale-deformed relativistic symmetries and diffeomorphisms in momentum space
• On limitations of the extent of inertial frames in non-commutative relativistic spacetimes
• Deformed Special Relativity from Asymptotically Safe Gravity
• Gravity in quantum spacetime
• Physical Constraints on Quantum Deformations of Spacetime Symmetries
• Constraining the loop quantum gravity parameter space from phenomenology
• $\kappa$-Minkowski star product in any dimension from symplectic realization
• Scalar Field theory in $\kappa$-Minkowski spacetime from twist
• Curved momentum spaces from quantum groups with cosmological constant
• Possible quantum gravity effects on the gravitational deflection of light
• Quantum groups and deformed special relativity
• Geometry of multi-particle systems with a relativistic deformed kinematics and the relative locality principle
• Approaching Space Time Through Velocity in Doubly Special Relativity
• Field theories on spaces with linear fuzziness
• Particle velocity in noncommutative space-time
• Deformed General Relativity and Torsion
• Deformed Carroll particle from 2+1 gravity
• Quantum kappa-deformed differential geometry and field theory
• Field theory amplitudes in a space with SU(2) fuzziness
• Kappa-deformation of phase space; generalized Poincare algebras and R-matrix
• Position space versions of Magueijo-Smolin doubly special relativity proposal and the problem of total momentum
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• Relativistic compatibility of the interacting $\kappa$-Poincaré model and implications for the relative locality framework
• Twisted (2+1) $\kappa$-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes
• Loop diagrams in space with SU(2) fuzziness
• Poisson gauge models and Seiberg-Witten map
• Resonant-bar detectors of gravitational wave as possible probe of the noncommutative structure of space
• Rainbow-like Black Hole metric from Loop Quantum Gravity
• Differential forms and k-Minkowski spacetime from extended twist
• Building a case for a Planck-scale-deformed boost action: the Planck-scale particle-localization limit
• On the semiduals of local isometry groups in 3d gravity
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Kappa - Poincare dispersion relations and the black hole radiation
• Long time black hole evaporation with bounded Hawking flux
• Localization and observers in $\varrho$-Minkowski spacetime
• Observables from spherically symmetric modified dispersion relations
• A note on DSR-like approach to space-time
• Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry
• Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries
• Graded contractions and bicrossproduct structure of deformed inhomogeneous algebras
• Particle and Antiparticle sectors in DSR1 and kappa-Minkowski space-time
• Lorentz Covariant k-Minkowski Spacetime
• Spectral dimensions and dimension spectra of quantum spacetimes
• Quantum geodesic flows and curvature
• Quasitriangular structure and twisting of the 2+1 bicrossproduct model
• A Novel "Magnetic" Field And Its Dual Non-Commutative Phase Space
• Towards (3+1) gravity through Drinfel'd doubles with cosmological constant
• Light-like $\kappa$-deformations and scalar field theory via Drinfeld twist
• Experimental test of Non-Commutative Quantum Gravity by VIP-2 Lead
• Quantum gravity on polygons and $\mathbb{R}\times {\mathbb{Z}}_n$ FLRW model
• AdS Poisson homogeneous spaces and Drinfel'd doubles
• Noncommutative spherically symmetric spacetimes at semiclassical order
• Effects of quantum deformation on the integer quantum Hall effect
• Quantum geodesics on $\lambda$-Minkowski spacetime
• Quantum walks, deformed relativity, and Hopf algebra symmetries
• Black hole as an Information Eraser
• On the 5D differential calculus and translation transformations in 4D kappa-Minkowski noncommutative spacetime
• Star Product and Invariant Integration for Lie type Noncommutative Spacetimes
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Hermitian realizations of kappa-Minkowski spacetime
• Beyond Fock space in three dimensional semiclassical gravity
• Scalar field in the Bianchi I: Non commutative classical and Quantum Cosmology
• Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz and Poincare algebras and their dual extensions
• Twisted BRST symmetry in gauge theories on $\kappa$-Minkowski
• Associative realizations of $\kappa$-deformed extended Snyder model
• Twisted bialgebroids versus bialgebroids from a Drinfeld twist
• A new Doubly Special Relativity theory from a quantum Weyl-Poincare algebra
• Dispersion relations in finite-boost DSR
• Classification of digital affine noncommutative geometries
• Fuzzy and discrete black hole models
• Vacuum energy and the cosmological constant problem in $\kappa$-Poincaré invariant field theories
• Double Quantization
• Single Extra Dimension from $\kappa$-Poincaré and Gauge Invariance
• Quantum mechanics on space with SU(2) fuzziness
• Causality and momentum conservation from relative locality
• Quantum perturbative solutions of extended Snyder and Yang models with spontaneous symmetry breaking
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Once again about quantum deformations of D=4 Lorentz algebra: twistings of q-deformation
• Poisson structure on a space with linear SU(2) fuzziness
• Blackbody radiation in κ-Minkowski spacetime
• Quantum $\kappa$-Poincaré Algebra from de Sitter Space of Momenta
• Cayley-Klein Lie bialgebras: Noncommutative spaces, Drinfel'd doubles and kinematical applications
• A group theoretic description of the $\kappa$-Poincaré Hopf algebra
• Non-commutative Fourier transform for the Lorentz group via the Duflo map
• Baryon asymmetry in the Universe resulting from Lorentz violation
• Two-dimensional gravity with an invariant energy scale
• Quantisation of Klein-Gordon field in $\kappa$ space-time: deformed oscillators and Unruh effect
• k-deformed Poincare algebras and quantum Clifford-Hopf algebras
• A short introduction to $\kappa$-deformation
• Quantum particles in non-commutative space-time: an identity crisis
• Extending general covariance: Moyal-type noncommutative manifolds
• Bicrossproduct structure of the null-plane quantum Poincare algebra
• Time-space noncommutativity and Casimir effect
• A bound on Planck-scale modifications of the energy-momentum composition rule from atomic interferometry
• Canonical k-Minkowski Spacetime
• Predictive description of Planck-scale-induced spacetime fuzziness
• A fundamental length as a candidate for dark energy: a DSR inspired FRW spacetime
• Effects of quantum deformation on the Jaynes-Cummings and anti-Jaynes-Cummings models
• Relativistic deformed kinematics from locality conditions in a generalized spacetime
• Two-body decays in deformed relativity
• $\kappa$-de Sitter and $\kappa$-Poincaré symmetries emerging from Chern-Simons (2+1)D gravity with a cosmological constant
• Accelerated horizons and Planck-scale kinematics
• Multi-particle systems in $\kappa$-Poincaré inspired by 2+1D gravity
• Fundamental physics in space: a Quantum-Gravity perspective
• Hopf-algebra description of noncommutative-spacetime symmetries
• Quantum algebras as quantizations of dual Poisson-Lie groups
• Coisotropic Lie bialgebras and complementary dual Poisson homogeneous spaces
• Twin Peaks: A possible signal in the production of resonances beyond special relativity
• Bicrossproduct approach to the Connes-Moscovici Hopf algebra
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Misleading inferences from discretization of empty spacetime: Snyder-noncommutativity case study
• Time delays, choice of energy-momentum variables and relative locality in doubly special relativity
• Vacuum energy from noncommutative models
• All noncommutative spaces of $\kappa$-Poincaré geodesics
• Noncommutativity and the Weak Cosmic Censorship
• A cosmological viewpoint on the correspondence between deformed phase-space and canonical quantization
• $\kappa$-Deformation of Poincaré Superalgebra with Classical Lorentz Subalgebra and its Graded Bicrossproduct Structure
• Classical electrodynamics on Snyder space
• Absorption of TeV Photons and $\kappa$-deformed Poincaré algebra
• Relative Locality in Curved Space-time
• Dirac operator on $\kappa$-Minkowski space bicovariant differential calculus and deformed U(1) gauge theory
• Kappa-deformed Dirac oscillator in an external magnetic field
• Snyder Space-Time: K-Loop and Lie Triple System
• Noncommutative spaces and covariant formulation of statistical mechanics
• Group of boost and rotation transformations with two observer-independent scales
• Statistical mechanics of free particles on space with Lie type noncommutativity
• The Weyl realizations of Lie algebras and left-right duality
• Compact $\kappa$-deformation and spectral triples
• Modified particle lifetimes as a signature of deformed relativity
• Generalized quantum phase spaces for the $\kappa$-deformed extended Snyder model
• Closedness of orbits in a space with SU(2) Poisson structure
• From Snyder space-times to doubly $\kappa$-dependent Yang quantum phase spaces and their generalizations
• Symmetries of $\kappa$ Minkowski space-time: A possibility of exotic momentum space geometry?
• A new perspective on Doubly Special Relativity
• Space-time thermodynamics in momentum dependent geometries
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• Quantum instability of gauge theories on $\kappa$-Minkowski space
• Photonic realization of the kappa-deformed Dirac equation
• $\kappa$-deformed BMS symmetry
• Quantum space and quantum completeness
• On the emergence of the structure of Physics
• Quantum Koszul formula on quantum spacetime
• Effective Chern-Simons actions of particles coupled to 3D gravity
• Aspects of perturbative quantum field theory on non-commutative spaces
• Lorentz Violation in Finsler Geometry
• Relativistic deformed kinematics: from flat to curved spacetimes
• Planck-scale deformation of CPT and particle lifetimes
• Duality Principle and Braided Geometry
• Triangular quasi-Hopf algebra structures on certain non-semisimple quantum groups
• The cosmological implications of a fundamental length: a DSR inspired de-Sitter spacetime
• Observers and Measurements in Noncommutative Spacetimes
• $\kappa$-deformations of D=3 conformal versus deformations of D=4 AdS symmetries
• $\kappa$--Rindler space
• From Barthel Randers Kropina Geometries to the Accelerating Universe: A Brief Review of Recent Advances in Finslerian Cosmology
• The quantum Poincare group from quantum group contraction
• Entropy bound for the photon gas in noncommutative spacetime
• Fractional quantum mechanics meets quantum gravity phenomenology
• Weakness of accelerator bounds on electron superluminality without a preferred frame
• Causal loop in the theory of relative locality
• Field theories on $\rho$-deformed Minkowski space-time
• Extended noncommutative Minkowski spacetimes and hybrid gauge symmetries
• Particle-antiparticle asymmetry in a relativistic deformed kinematics
• Classical r-matrices via semidualisation
• Cornwall-Jackiw-Tomboulis effective potential for canonical noncommutative field theories
• Central tetrads and quantum spacetimes
• Quantization of fluctuations in DSR: the two-point function and beyond
• Quantum Kaluza-Klein theory with $M_2(\mathbb{C})$
• Twisting cocycles in fundamental representation and triangular bicrossproduct Hopf algebras
• Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
• Quantum symmetries in 2+1 dimensions: Carroll, (a)dS-Carroll, Galilei and (a)dS-Galilei
• Finite entanglement entropy and spectral dimension in quantum gravity
• Doubly Special Relativity with light-cone deformation
• Relativistic Planck-scale polymer
• Emergence of maximal acceleration from non-commutativity of space-time
• Heisenberg Evolution in a Quantum Theory of Noncommutative Fields
• Noncommutative Parameters of Quantum Symmetries and Star Products
• Hidden entanglement at the Planck scale: loss of unitarity and the information paradox
• Scaling Limit of the Noncommutative Black Hole
• Multi-particle systems in quantum spacetime and a novel challenge for center-of-mass motion
• Past and future blurring at fundamental length scale
• Dirac theory on a space with linear Lie type fuzziness
• Quantum groups and braid groups as fundamental symmetries
• A Field Theory Model With a New Lorentz-Invariant Energy Scale
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Poincaré Covariant k-Minkowski Spacetime
• Maximal acceleration in non-commutative space-time and its implications
• Gauge theory on a space with linear Lie type fuzziness
• Deformed phase spaces with group valued momenta
• Early universe thermostatistics in curved momentum spaces
• UV dimensional reduction to two from group valued momenta
• On Hopf algebroid structure of kappa-deformed Heisenberg algebra
• Central force problem in space with SU(2) Poisson structure
• Weak equivalence principle and nonrelativistic limit of general dispersion relations
• A Stochastic Origin of Spacetime Non-Commutativity
• On the Notion of Noncommutative Submanifold
• Quantum Riemannian geometry of the discrete interval and q-deformation
• Uncertainty of Velocity in kappa-Minkowski Spacetime
• $\kappa$-Galilean and $\kappa$-Carrollian noncommutative spaces of worldlines
• Quantum superpositions of the speed of light
• NC Wilson lines and the inverse Seiberg-Witten map for nondegenerate star products
• Thermal and spectral dimension of (generalized) Snyder noncommutative spacetimes
• BMS algebras in 4 and 3 dimensions, their quantum deformations and duals
• Neutrinos as possible probes for quantum gravity
• On Charge Conservation and The Equivalence Principle in the Noncommutative Spacetime
• Muon accelerators -- Muon lifetime measurements as window to Planck scale physics
• Trace of phase-space noncommutativity in the response of a free particle to linearized gravitational waves
• Dual Kappa Poincare Algebra
• Quantum geometry and quantization on U(u(2)) background. Noncommutative Dirac monopole
• Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions
• Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra
• Lorentz Symmetry and Ultra-High-Energy Cosmic Rays
• The noncommutative space of light-like worldlines
• $N=2$ quantum chiral superfields and quantum super bundles
• Bicrossproduct construction versus Weyl-Heisenberg algebra
• Symmetries of the Dirac quantum walk and emergence of the de Sitter group
• The Theory of a Quantum Noncanonical Field in Curved Spacetimes
• Longitudinal and transverse relativity of spacetime locality in Planck-scale-deformed phase spaces
• Testing kappa-Poincare' with neutral kaons
• $\kappa$-General-Relativity I: a Non-Commutative GR Theory with the $\kappa$-Minkowski Spacetime as its Flat Limit
• $\kappa$-deformed power spectrum and modified Unruh temperature
• Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries
• Towards new relativistic doubly $\kappa$-deformed D=4 quantum phase spaces
• Cosmic Neutrinos as a Window to Departures from Special Relativity
• Covariant formulation of Noether's Theorem for translations on kappa-Minkowski spacetime
• Relativistic Generalized Uncertainty Principle and Its Implications
• On the spectral and homological dimension of k-Minkowski space
• Quantization of Spacetime Based on Spacetime Interval Operator
• Generalized Heisenberg algebra, realizations of the $\mathfrak{gl}(n)$ algebra and applications
• Photon gas thermodynamics in dS and AdS momentum spaces
• Fate of $\kappa$-Minkowski space-time in non-relativistic (Galilean) and ultra-relativistic (Carrollian) regimes
• Yang-Mills field from fuzzy sphere quantum Kaluza-Klein model
• Quantum groups and noncommutative spacetimes with cosmological constant
• Quantum Klein Space and Superspace
• How does Casimir energy fall in $\kappa$-deformed space-time?
• Doubly Special Relativity: A Kinematics of Quantum Gravity?
• Exploring black hole mechanics in cotangent bundle geometries
• Twisting loops and global momentum non-conservation in Relative Locality
• Generalization of Weyl realization to a class of Lie superalgebras
• Classification of differentials and Cartan calculus on bicrossproducts
• Vector Field Twisting of Lie-Algebras
• Braided Tensor Products and the Covariance of Quantum Noncommutative Free Fields
• Orientability of loop processes in relative locality
• Induced Representations of Quantum Kinematical Algebras and Quantum Mechanics
• Centripetal force on Casimir energies in $\kappa$-deformed rotating frame
• Quantum causality constraints on kappa-Minkowski space-time
• T-Minkowski noncommutative spacetimes II: classical field theory
• Total momentum and other Noether charges for particles interacting in a quantum spacetime
• Noncommutative kappa-Minkowski phi4 theory: Construction, properties and propagation
• Noncommutative spacetime symmetries from covariant quantum mechanics
• On the Poisson structure related to $\kappa$-Poincaré Group
• Anti-de Sitter Momentum Space in 3D and 4D Quantum Gravity
• Twist deformations leading to kappa-Poincare Hopf algebra and their application to physics
• Electroweak symmetries from the topology of deformed spacetime with minimal length scale
• Lie Particle And Its Batalin-Tyutin Extension
• Some Features of Scattering Problem in a $\kappa$-Deformed Minkowski Spacetime
• Towards a topological (dual of) quantum $\kappa$-Poincaré group
• Modified Lorentz transformations in deformed special relativity
• On the bicrossproduct structures for the ${\mathcal{U}}_{\lambda }(is{o}_{{\omega }_2...{\omega }_N}(N))$ family of algebras
• Projective representation of k-Galilei group
• Lie algebraic noncommuting structures from reparametrisation symmetry
• Could LIV/noncommutativity alleviate the cosmological constant problem
• $\kappa$-Poincaré phase space: speed of massless particles and relativity of spacetime locality
• Wave Propagation and IR/UV Mixing in Noncommutative Spacetimes
• Gravity's weight on worldline fuzziness
• T-Minkowski noncommutative spacetimes I: Poincaré groups, differential calculi and braiding
• alpha^star-Cohomology and Classification of Translation-Invariant Non-Commutative Quantum Field Theories
• Quantisation of $\kappa$-deformed Dirac equation
• Force in Kappa-Deformed Relativistic Dynamics
• Digital quantum groups
• Global Space-Time Symmetries of Quantized Euclidean and Minkowski Superspaces
• The Weyl-Mellin quantization map for $\kappa$-Minkowski Noncommutative Spacetime
• Testing the universality of quantum gravity theories with cosmic messengers in the context of DSR theories
• From quantum deformations of relativistic symmetries to modified kinematics and dynamics
• Noncommutative Extension of Minkowski Spacetime and Its Primary Application
• The Majid-Ruegg model and the Planck scales
• Noncommutative Spacetime Realized in $Ad{S}_{n+1}$ Space
• Eigenvalue problem for radial potentials in space with SU(2) fuzziness
• Spacetime defects and group momentum space
• Maxwell's equations and Lorentz force in doubly special relativity
• Effective action in DSR1 quantum field theory
• Charge specific baryon mass relations with deformed SU_q(3) flavor symmetry
• Quantum Gravity models - brief conceptual summary
• Parity at the Planck scale
• DSR-relativistic spacetime picture and the phenomenology of Planck-scale-modified time dilation
• Path integral quantization of a spinning particle
• Twisting kappa-deformed phase space
• Entropic force and bouncing behaviour in $\kappa$-Minkowski space-time
• Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups
• Vulcanized Vortex
• Fuzzy worldlines with $\kappa$-Poincaré symmetries
• Spinorial Snyder and Yang Models From Superalgebras And Noncommutative Quantum Superspaces
• Quantum causality in $\kappa$-Minkowski and related constraints
• Noncommutative spacetimes versus noncommutative spaces of geodesics
• Non-coboundary Poisson-Lie structures on the book group
• Time dependent transitions with time-space noncommutativity & its implications in Quantum Optics
• The universe is not a Lie, but actually an Hopf, algebra
• Photon Absorption in a Doubly Special Relativity Model with Undeformed Free Propagation and Total Momentum Conservation
• Topics in Noncommutative Gauge Theories and Deformed Relativistic Theories
• 5D Differential Calculus and Noether Analysis of Translation Symmetries in kappa-Minkowski Noncommutative Spacetime
• Kinetic gases in static spherically symmetric modified dispersion relations
• The covariant and on-shell statistics in kappa-deformed spacetime
• $\kappa$-General-Relativity II: An Astrophysical Observable from a 2-Body system
• Quantization of subgroups of the affine group
• Poisson Principal Bundles
• Coherence and Entanglement in a Non-commutative Spacetime
• Deformations of spacetime and internal symmetries
• A relation between deformed superspace and Lee-Wick higher-derivative theories
• Could we observe the discreteness of Quantum-Gravity length and area operators ?
• Semidual Kitaev lattice model and tensor network representation
• Experimental Bounds on Deformed Muon Lifetime Dilation
• Asymmetry in momentum space: restoring $\mathcal{C}\mathcal{P}\mathcal{T}$ invariance of $\kappa$-field theory
• Operator Entanglement from Non-Commutative Symmetries
• On Carrollian and Galilean contractions of BMS algebra in 3 and 4 dimensions
• Bounds on Large Extra Dimensions from the Generalized Uncertainty Principle
• A winding number analysis of Schwarzschild black hole stability in light of Planck-scale modified kinematics
• Doubly Special Relativity and quantum gravity phenomenology
• Quantum Deformations of Space-Time Symmetries with Mass-Like Deformation Parameter
• Unruh effect using Doppler shift method in DSR framework
• Primitively divergent diagrams in $\kappa$-deformed scalar field with quartic self-interaction
• Quantum double and $\kappa$-Poincaré symmetries in (2+1)-gravity and Chern-Simons theory
• Braided Statistics from Abelian Twist in $\kappa$-Minkowski Spacetime
• Polyhedron phase space using 2-groups: kappa-Poincare as a Poisson 2-group
• N=1/2 Global SUSY: R-Matrix Approach
• Twisted Rindler space-times
• Covariant four dimensional differential calculus in $\kappa$-Minkowski
• 3-dimensional $\Lambda$-BMS Symmetry and its Deformations
• Gauge Theories on Open Lie Algebra Non-Commutative Spaces