Wedge-Local Quantum Fields and Noncommutative Minkowski Space
arXiv:0706.3992 · doi:10.1088/1126-6708/2007/11/012
Abstract
Within the setting of a recently proposed model of quantum fields on noncommutative Minkowski spacetime, the consequences of the consistent application of the proper, untwisted Poincare group as the symmetry group are investigated. The emergent model contains an infinite family of fields which are labelled by different noncommutativity parameters, and related to each other by Lorentz transformations. The relative localization properties of these fields are investigated, and it is shown that to each field one can assign a wedge-shaped localization region of Minkowski space. This assignment is consistent with the principles of covariance and locality, i.e. fields localized in spacelike separated wedges commute. Regarding the model as a non-local, but wedge-local, quantum field theory on ordinary (commutative) Minkowski spacetime, it is possible to determine two-particle S-matrix elements, which turn out to be non-trivial. Some partial negative results concerning the existence of observables with sharper localization properties are also obtained.
Version to appear in JHEP, 27 pages
References in corpus (18)
- 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
- Lectures on Loop Quantum Gravity
- General Properties of Noncommutative Field Theories
- Construction of Quantum Field Theories with Factorizing S-Matrices
- On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
- Polarization-Free Generators and the S-Matrix
- String-localized Quantum Fields and Modular Localization
- Local fields in boundary conformal QFT
- Modular Localization and the Bootstrap-Formfactor Program
- Modular Nuclearity and Localization
- Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory
- String-- and Brane--Localized Causal Fields in a Strongly Nonlocal Model
- Quantum Fields on the Groenewold-Moyal Plane: C, P, T and CPT
- Spin, Statistics, and Reflections, II. Lorentz Invariance
Cited by in corpus (50)
- Soliton gases and generalized hydrodynamics
- Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories
- Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
- Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane
- A Perspective on Constructive Quantum Field Theory
- Geometrizing
- Construction of wedge-local nets of observables through Longo-Witten endomorphisms
- Deformations of quantum field theories and integrable models
- On second quantization on noncommutative spaces with twisted symmetries
- Non-commutative Geometry from Perturbative Quantum Gravity
- Characterization of local observables in integrable quantum field theories
- Noncommutative Quantum Field Theory: A Confrontation of Symmetries
- Asymptotic completeness in a class of massless relativistic quantum field theories
- Deformations of quantum field theories on spacetimes with Killing vector fields
- Construction of wedge-local nets of observables through Longo-Witten endomorphisms. II
- Symmetries of noncommutative scalar field theory
- Twisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model
- Field Theory on Curved Noncommutative Spacetimes
- Localization and Entanglement in Relativistic Quantum Physics
- Deformations of Fermionic Quantum Field Theories and Integrable Models
- Wedge-local fields in integrable models with bound states
- Duality and Braiding in Twisted Quantum Field Theory
- Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes
- On the equivalence of two deformation schemes in quantum field theory
- Quantum Mechanical Effects from Deformation Theory
- Wedge-Local Quantum Fields on a Nonconstant Noncommutative Spacetime
- An Algebraic Jost-Schroer Theorem for Massive Theories
- Deformations of quantum field theories on de Sitter spacetime
- Noncommutative deformations of quantum field theories, locality, and causality
- Wedge locality and asymptotic commutativity
- Failure of microcausality in noncommutative field theories
- N-Particle Scattering in Relativistic Wedge-Local Quantum Field Theory
- Propagators and Matrix Basis on Noncommutative Minkowski Space
- On the consequences of twisted Poincare' symmetry upon QFT on Moyal noncommutative spaces
- Deformations of half-sided modular inclusions and non-local chiral field theories
- Self-Adjointness of Deformed Unbounded Operators
- Linear hyperbolic PDEs with non-commutative time
- Uniformly Accelerated Observer in Moyal Spacetime
- Wedge Local Deformations of Charged Fields leading to Anyonic Commutation Relations
- Strict deformations of quantum field theory in de Sitter spacetime
- A Deformation Quantization for Non-Flat Spacetimes and Applications to QFT
- Asymptotic Completeness in a Class of Massive Wedge-Local Quantum Field Theories in any Dimension
- A Poincaré Covariant Noncommutative Spacetime?
- Relativistic Corrections to the Moyal-Weyl Spacetime
- Curving Flat Space-Time by Deformation Quantization?
- Spontaneous breaking of symmetry in Moyal spacetime with twisted Poincaré symmetry
- Strict Almost Non-Abelian Deformations
- A Quantum Energy Inequality for a Non-commutative QFT
- Complete Minimal Form Factors for Irrelevant Deformations of Integrable Quantum Field Theory
- Wick rotation for quantum field theories on degenerate Moyal space(-time)