Untwisting Noncommutative R^d and the Equivalence of Quantum Field Theories

Abstract

We show that there is a duality exchanging noncommutativity and non-trivial statistics for quantum field theory on R^d. Employing methods of quantum groups, we observe that ordinary and noncommutative R^d are related by twisting. We extend the twist to an equivalence for quantum field theory using the framework of braided quantum field theory. The twist exchanges both commutativity with noncommutativity and ordinary with non-trivial statistics. The same holds for the noncommutative torus.

19 pages, LaTeX with AMS and XY-Pic macros; references added

References in corpus (4)

• String Theory and Noncommutative Geometry
• The quantum structure of spacetime at the Planck scale and quantum fields
• Noncommutative Perturbative Dynamics
• Noncommutative String Theory, the R-Matrix, and Hopf Algebras

Cited by in corpus (114)

• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Noncommutative Geometry and Gravity
• Symmetry, Gravity and Noncommutativity
• Spin and Statistics on the Groenewold-Moyal Plane: Pauli-Forbidden Levels and Transitions
• New Lie-Algebraic and Quadratic Deformations of Minkowski Space from Twisted Poincare Symmetries
• Twisted Statistics in kappa-Minkowski Spacetime
• Comments on noncommutative gravity
• Combinatorial Hopf algebras in quantum field theory I
• Diffeomorphisms in group field theories
• Statistics and UV-IR Mixing with Twisted Poincare Invariance
• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• Twisted Gauge Theories
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Twisting all the way: from Classical Mechanics to Quantum Fields
• Towards Quantum Noncommutative $\kappa$-deformed Field Theory
• UV-IR Mixing in Non-Commutative Plane
• Multi-orientable Group Field Theory
• Twisted Noncommutative Field Theory with the Wick-Voros and Moyal Products
• Twisted Galilean symmetry and the Pauli principle at low energies
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Noncommutative field theory with the Wick-Voros product
• Remarks on twisted noncommutative quantum field theory
• Space-time symmetry of noncommutative field theory
• Twist to close
• kappa-deformed Spacetime From Twist
• Quantum Fields on the Groenewold-Moyal Plane
• Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane
• Drinfeld-Twisted Supersymmetry and Non-Anticommutative Superspace
• Quantum field theory and Hopf algebra cohomology
• Twisted Poincaré Invariant Quantum Field Theories
• Twist-Deformed Supersymmetries in Non-Anticommutative Superspaces
• Rainbow statistics
• Noncommutative spacetime symmetries: Twist versus covariance
• Noncommutative Two Dimensional Gravities
• Noncommutative Field Theory from twisted Fock space
• Twisted Conformal Symmetry in Noncommutative Two-Dimensional Quantum Field Theory
• Noncommutative Symmetries and Gravity
• Gauge theories on quantum spaces
• Twisted Covariant Noncommutative Self-dual Gravity
• Quantum Fields with Noncommutative Target Spaces
• On second quantization on noncommutative spaces with twisted symmetries
• Drinfeld Twist and General Relativity with Fuzzy Spaces
• Braided $L_{\infty }$-Algebras, Braided Field Theory and Noncommutative Gravity
• Canonical and Lie-algebraic twist deformations of Galilei algebra
• Noncommutative Quantum Field Theory: A Confrontation of Symmetries
• Classical mechanics of many particles defined on canonically deformed nonrelativistic space-time
• Quantum statistics and noncommutative black holes
• Testing Noncommutative Spacetimes and Violations of the Pauli Exclusion Principle with underground experiments
• Position-dependent noncommutative products: classical construction and field theory
• Classical Mechanics on Noncommutative Space with Lie-algebraic Structure
• Infinity Operads and Monoidal Categories with Group Equivariance
• Braided Symmetries in Noncommutative Field Theory
• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• Noncommutative Linear Sigma Models
• Causality and statistics on the Groenewold-Moyal plane
• Twisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Theta-twisted Gravity
• Quantum Fields on the Groenewold-Moyal Plane: C, P, T and CPT
• The Quantum Geometry of Spin and Statistics
• Jordanian Twist Quantization of D=4 Lorentz and Poincare Algebras and D=3 Contraction Limit
• N=1/2 Deformations of Chiral Superspaces from New Quantum Poincare and Euclidean Superalgebras
• Canonical and Lie-algebraic twist deformations of $\kappa$-Poincare and contractions to $\kappa$-Galilei algebras
• Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra
• QFT with Twisted Poincaré Invariance and the Moyal Product
• Global Symmetries of Noncommutative Space-time
• Duality and Braiding in Twisted Quantum Field Theory
• Reality in Noncommutative Gravity
• Noncommutative Quantization for Noncommutative Field Theory
• Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes
• Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces
• Dynamical origin of the ${\star }_{\theta }$-noncommutativity in field theory from quantum mechanics
• Deformed Schrodinger symmetry on noncommutative space
• Tensor calculus on noncommutative spaces
• Translational-invariant noncommutative gauge theory
• Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
• The Cutkosky rule of three dimensional noncommutative field theory in Lie algebraic noncommutative spacetime
• Noncommutative Gravity and the *-Lie algebra of diffeomorphisms
• UV/IR mixing as a twisted Poincaré anomaly
• Dispersion relations in the noncommutative ϕ^3 and Wess-Zumino model in the Yang-Feldman formalism
• Twisted invariances of noncommutative gauge theories
• Canonical, Lie-algebraic and quadratic twist deformations of Galilei group
• Lehmann-Symanzik-Zimmermann S-Matrix elements on the Moyal Plane
• Deformations of Euclidean Supersymmetries
• Triangular quasi-Hopf algebra structures on certain non-semisimple quantum groups
• Z^0 \to 2γand the Twisted Coproduct of the Poincaré Group
• Batalin-Vilkovisky quantization of fuzzy field theories
• Poincare' Quasi-Hopf Symmetry and Non-Associative Spacetime Algebra from Twisted Gauge Theories
• Heat kernel of non-minimal gauge field kinetic operators on Moyal plane
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time
• Twist Quantization of String and B Field Background
• Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory
• Symplectic Deformations, Non Commutative Scalar Fields and Fractional Quantum Hall Effect
• On Charge Conservation and The Equivalence Principle in the Noncommutative Spacetime
• Interacting Quantum Topologies and the Quantum Hall Effect
• Canonical Quantization, Space-Time Noncommutativity and Deformed Symmetries in Field Theory
• Braided Field Quantization from Quantum Poincare Covariance
• Noncommutative Sprott systems and their jerk dynamics
• A Deformation Quantization for Non-Flat Spacetimes and Applications to QFT
• Global Space-Time Symmetries of Quantized Euclidean and Minkowski Superspaces
• Noncommutative Geometry: Fuzzy Spaces, the Groenewold-Moyal Plane
• T-Minkowski noncommutative spacetimes I: Poincaré groups, differential calculi and braiding
• T-Minkowski noncommutative spacetimes II: classical field theory
• On the Correspondence between Poincaré Symmetry of Commutative QFT and Twisted Poincaré Symmetry of Noncommutative QFT
• Quantum harmonic oscillator in a time dependent noncommutative background
• Generalized twist deformations of Poincare and Galilei quantum groups
• Braided Tensor Products and the Covariance of Quantum Noncommutative Free Fields
• A note on the implementation of Poincaré symmetry in noncommutative field theory
• Two ${\theta }_{\mu \nu }$ -deformed covariant relativistic quantum phase spaces as Poincare-Hopf algebroids
• Space-Time Diffeomorphisms in Noncommutative Gauge Theories
• N=1/2 Global SUSY: R-Matrix Approach
• Noncommutative scalar fields from symplectic deformation