New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications

Abstract

We present a systematic framework for noncommutative (NC) QFT within the new concept of relativistic invariance based on the notion of twisted Poincaré symmetry (with all 10 generators), as proposed in ref. [7]. This allows to formulate and investigate all fundamental issues of relativistic QFT and offers a firm frame for the classification of particles according to the representation theory of the twisted Poincaré symmetry and as a result for the NC versions of CPT and spin-statistics theorems, among others, discussed earlier in the literature. As a further application of this new concept of relativism we prove the NC analog of Haag's theorem.

15 pages

References in corpus (11)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• The quantum structure of spacetime at the Planck scale and quantum fields
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Space-Time Noncommutative Field Theories And Unitarity
• Space/Time Non-Commutativity and Causality
• General Properties of Noncommutative Field Theories
• Spin-Statistics and CPT Theorems in Noncommutative Field Theory
• Non-linear Vacuum Phenomena in Non-commutative QED
• Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory

Cited by in corpus (188)

• Noncommutative Geometry and Gravity
• Symmetry, Gravity and Noncommutativity
• Kappa-Minkowski space-time and the star product realizations
• New realizations of Lie algebra kappa-deformed Euclidean space
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• Corrections to Schwarzschild Solution in Noncommutative Gauge Theory of Gravity
• New Lie-Algebraic and Quadratic Deformations of Minkowski Space from Twisted Poincare Symmetries
• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• Comments on noncommutative gravity
• Voros product, Noncommutative Schwarzschild Black Hole and Corrected Area Law
• Covariant realizations of kappa-deformed space
• Emergent Gravity from Noncommutative Spacetime
• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• Topics in Noncommutative Geometry Inspired Physics
• Fock space, quantum fields and kappa-Poincaré symmetries
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Yang-Baxter $\sigma$-models, conformal twists, and noncommutative Yang-Mills theory
• Twisting all the way: from Classical Mechanics to Quantum Fields
• UV-IR Mixing in Non-Commutative Plane
• CPT Violation Does Not Lead to Violation of Lorentz Invariance and Vice Versa
• Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics
• A Realization of the Cohen-Glashow Very Special Relativity
• Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
• Fractional and noncommutative spacetimes
• On Black Holes and Cosmological Constant in Noncommutative Gauge Theory of Gravity
• Conformal Twists, Yang-Baxter $\sigma$-models & Holographic Noncommutativity
• Generalized kappa-deformed spaces, star-products, and their realizations
• Symplectic geometry and Noether charges for Hopf algebra space-time symmetries
• Twist and Spin-Statistics Relation in Noncommutative Quantum Field Theory
• Remarks on twisted noncommutative quantum field theory
• Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT)
• Twist to close
• Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory
• Drinfeld-Twisted Supersymmetry and Non-Anticommutative Superspace
• kappa-deformed Spacetime From Twist
• Quantum Fields on the Groenewold-Moyal Plane
• Non-Commutative Geometry and Twisted Conformal Symmetry
• NC $SO(2,3{)}_{\star }$ gravity: noncommutativity as a source of curvature and torsion
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Twist-Deformed Supersymmetries in Non-Anticommutative Superspaces
• Noncommutative Differential Forms on the kappa-deformed Space
• Rainbow statistics
• Instantons and Emergent Geometry
• Braided quantum field theories and their symmetries
• Fundamental length in quantum theories with PT-symmetric Hamiltonians
• Quantum fields, non-locality and quantum group symmetries
• Twist as a Symmetry Principle and the Noncommutative Gauge Theory Formulation
• Noncommutative Field Theory from twisted Fock space
• Twisted Conformal Symmetry in Noncommutative Two-Dimensional Quantum Field Theory
• $\kappa$-Poincaré invariant quantum field theories with KMS weight
• Differential structure on kappa-Minkowski space, and kappa-Poincare algebra
• Newton equation for canonical, Lie-algebraic and quadratic deformation of classical space
• Gravitational Instantons from Gauge Theory
• Gauge theories on quantum spaces
• Riemannian Geometry of Noncommutative Surfaces
• On the Landau system in noncommutative phase-space
• Noncommutative Spacetime in Very Special Relativity
• Noncommutative Geometries and Gravity
• On second quantization on noncommutative spaces with twisted symmetries
• Noncommutative BTZ Black Hole in Polar Coordinates
• Drinfeld Twist and General Relativity with Fuzzy Spaces
• Noncommutative Quantum Field Theory: A Confrontation of Symmetries
• Electric Chern-Simons term, enlarged exotic Galilei symmetry and noncommutative plane
• Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action
• Failure of microcausality in quantum field theory on noncommutative spacetime
• Noncommutative spaces, the quantum of time and the Lorentz symmetry
• An Interpretation of Noncommutative Field Theory in Terms of a Quantum Shift
• Noncommutative Field Theory on Homogeneous Gravitational Waves
• Ramifications of Lineland
• Quasinormal Modes in Noncommutative Schwarzschild black holes
• Particle phenomenology on noncommutative spacetime
• Diffeomorphism covariant star products and noncommutative gravity
• Non-Pauli Effects from Noncommutative Spacetimes
• Noncommutative Field Theory from Quantum Mechanical Space-Space Noncommutativity
• Causality and statistics on the Groenewold-Moyal plane
• Field theory amplitudes in a space with SU(2) fuzziness
• Noncommutative fields and actions of twisted Poincare algebra
• Quantum Fields on the Groenewold-Moyal Plane: C, P, T and CPT
• Theta-twisted Gravity
• Gauging the twisted Poincare symmetry as noncommutative theory of gravitation
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Lorentz Covariant k-Minkowski Spacetime
• Non-commutative Quantum Mechanics in Three Dimensions and Rotational Symmetry
• QFT with Twisted Poincaré Invariance and the Moyal Product
• Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra
• Twisted statistics and the structure of Lie-deformed Minkowski spaces
• Twist Deformation of Rotationally Invariant Quantum Mechanics
• Noncommutative gravity and the relevance of the $\theta$-constant deformation
• Dirac equation on coordinate dependent noncommutative space-time
• Global Symmetries of Noncommutative Space-time
• Causal sets and conservation laws in tests of Lorentz symmetry
• Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation
• Deformed conformal and super-Poincaré symmetries in the non-(anti)commutative spaces
• Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces
• Infrared cutoffs and the adiabatic limit in noncommutative spacetime
• Quantum particles in non-commutative space-time: an identity crisis
• Scattering in three-dimensional fuzzy space
• Tensor calculus on noncommutative spaces
• The Noncommutative Doplicher-Fredenhagen-Roberts-Amorim Space
• Dynamical origin of the ${\star }_{\theta }$-noncommutativity in field theory from quantum mechanics
• Ultrahyperfunctional Approach to Non-Commutative Quantum Field Theory
• Analogy between the Schwarzschild solution in a noncommutative gauge theory and the Reissner-Nordström metric
• Thermodynamics of a charged particle in a noncommutative plane in a background magnetic field
• Twisted conformal algebra related to $\kappa$-Minkowski space
• A Noncommutative Version of the Minimal Supersymmetric Standard Model
• Supersymmetric Lorentz invariant deformations of superspaces
• Voros product, noncommutative inspired Reissner-Nordstr{ö}m black hole and corrected area law
• Induced entanglement entropy of harmonic oscillators in noncommutative phase space
• Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
• Analyticity of the Scattering Amplitude, Causality and High-Energy Bounds in Quantum Field Theory on Noncommutative Space-Time
• Dirac field and gravity in NC $SO(2,3{)}_{\star }$ model
• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• Gauge field theories with covariant star-product
• Symmetries in noncommutative field theories: Hopf versus Lie
• Twisted invariances of noncommutative gauge theories
• Canonical, Lie-algebraic and quadratic twist deformations of Galilei group
• Noncommutative field with constant background fields and neutral fermion
• Thermodynamic Properties of Yukawa-Schwarzschild Black Hole in Non-commutative Gauge Gravity
• Pauli equation on noncommutative plane and the Seiberg-Witten map
• Two-photon annihilation of singlet cold dark matters due to noncommutative space-time
• Lehmann-Symanzik-Zimmermann S-Matrix elements on the Moyal Plane
• Magnetic Monopole in Noncommutative Space-Time and Wu-Yang Singularity-Free Gauge Transformations
• Path integral action of a particle in a magnetic field in the noncommutative plane and the Aharonov-Bohm effect
• Noncommutative Brownian motion
• Gravitational probe of quantum spacetime
• On the consequences of twisted Poincare' symmetry upon QFT on Moyal noncommutative spaces
• Light-Like Noncommutativity, Light-Front Quantization and New Light on UV/IR Mixing
• Relativistic Particles on Quantum Space-time
• Heat kernel of non-minimal gauge field kinetic operators on Moyal plane
• Noncommutative Time in Quantum Field Theory
• Non-anticommutative Supersymmetric Field Theory and Quantum Shift
• On Twist Quantizations of D=4 Lorentz and Poincare Algebras
• Path integral action and Chern-Simons quantum mechanics in noncommutative plane
• Twists of quantum groups and noncommutative field theory
• Källén-Lehmann representation of noncommutative quantum electrodynamics
• On Charge Conservation and The Equivalence Principle in the Noncommutative Spacetime
• The E(2) Particle
• Space-time noncommutativity with a bifermionic parameter
• One-loop unitarity of scalar field theories on Poincare invariant commutative nonassociative spacetimes
• Voros product and the Pauli principle at low energies
• Two-particle system in Coulomb potential for twist-deformed space-time
• Noncommutative Reissner-Nordstrøm Black hole
• Generating of additional force terms in Newton equation by twist-deformed Hopf algebras and classical symmetries
• Noncommutative Deformation of Spinor Zero Mode and ADHM Construction
• Canonical Deformation of $N=2$ $Ad{S}_4$ SUGRA
• Microcausality of spin-induced noncommutative theories
• An Arena for Model Building in the Cohen-Glashow Very Special Relativity
• Noncommutative $SO(2,3{)}_{\star }$ Gauge Theory of Gravity
• Canonical Quantization, Space-Time Noncommutativity and Deformed Symmetries in Field Theory
• The Inhomogeneous Invariance Quantum Supergroup of Supersymmetry Algebra
• $\kappa$-deformed power spectrum and modified Unruh temperature
• Signatures of New Physics from HBT Correlations in UHECRs
• Global Space-Time Symmetries of Quantized Euclidean and Minkowski Superspaces
• The coordinate coherent states approach revisited
• The Henon-Heiles system defined on Lie-algebraically deformed Galilei space-time
• Connes spectral distance and nonlocality of generalized noncommutative phase spaces
• Noncommutative Geometry: Fuzzy Spaces, the Groenewold-Moyal Plane
• Path-integral action of a particle in the noncommutative phase-space
• On the Correspondence between Poincaré Symmetry of Commutative QFT and Twisted Poincaré Symmetry of Noncommutative QFT
• Twist deformations of Newtonian Schwarzschild-(Anti-)de Sitter classical system
• Twisted bosonization in two dimensional noncommutative spacetime
• Conservation law in noncommutative geometry -- Application to spin-orbit coupled systems
• Study on Noncommutative Representations of Galilean Generators
• A note on the implementation of Poincaré symmetry in noncommutative field theory
• Gauge Theories and Non-Commutative Geometry
• Space-Time Diffeomorphisms in Noncommutative Gauge Theories
• Equivalent forces in Newton equation from twist deformations and noninertial coordinate frames
• Time dependent transitions with time-space noncommutativity & its implications in Quantum Optics
• Discussion on Lorentz Invariance Violation of Non-commutative Field Theory and Neutrino Oscillation
• A noncommutative geometric approach to the quantum structure of spacetime
• Renormalization of Noncommutative Quantum Field Theories
• The energy-momentum conservation law in two-particle system for twist-deformed Galilei Hopf algebras
• Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory. II
• Noncommutative spaces with twisted symmetries and second quantization
• Pauli energy spectrum for twist-deformed space-time
• Deformation quantization for systems with second-class constraints in deformed fermionic phase space
• Curvature, area and Gauss-Bonnet formula of the Moyal sphere
• A relation between deformed superspace and Lee-Wick higher-derivative theories
• ${\pi }^{+}{\pi }^{+}$ and ${\pi }^{+}{\pi }^{-}$ colliding in noncommutative space
• Torsion-induced spin precession
• Cryptohermitian Hamiltonians on graphs. II. Hermitizations
• N=1/2 Global SUSY: R-Matrix Approach
• Spectra of disc operator for twisted acceleration-enlarged Newton-Hooke space-times
• On 2d gravity and parallel transport field equation on quantum sphere
• Theories on noncommutative spaces and deformed symmetries
• Aspects of noncommutativity in field theory, strings and membranes
• On the Non-Flatness Nature of Noncommutative Minkowski Spacetime and the Singular Behavior of Probes
• Massless Chiral Supermultiplets of Higher Spins and the $\theta$-Twistor