Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing

Abstract

We show that the Ultraviolet/Infrared mixing of noncommutative field theories with the Gronewold-Moyal product, whereby some (but not all) ultraviolet divergences become infrared, is a generic feature of translationally invariant associative products. We find, with an explicit calculation that the phase appearing in the nonplanar diagrams is the one given by the commutator of the coordinates, the semiclassical Poisson structure of the non commutative spacetime. We do this with an explicit calculation for represented generic products.

24 pages, 1 figure

References in corpus (22)

• String Theory and Noncommutative Geometry
• Deformation quantization of Poisson manifolds, I
• Noncommutative Perturbative Dynamics
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Space-Time Noncommutative Field Theories And Unitarity
• A Gravity Theory on Noncommutative Spaces
• Deformed Coordinate Spaces; Derivatives
• Twisting all the way: from Classical Mechanics to Quantum Fields
• Time-ordered Perturbation Theory on Noncommutative Spacetime: Basic Rules
• Ultraviolet Finite Quantum Field Theory on Quantum Spacetime
• Time-ordered Perturbation Theory on Noncommutative Spacetime II: Unitarity
• Infinitely many star products to play with
• On $\kappa$-Deformation and UV/IR Mixing
• Twisted Noncommutative Field Theory with the Wick-Voros and Moyal Products
• Noncommutative field theory with the Wick-Voros product
• On the ultraviolet behaviour of quantum fields over noncommutative manifolds
• Space/time noncommutative field theories and causality
• Non-Relativistic Non-Commutative Field Theory and UV/IR Mixing
• Heat-Kernel Approach to UV/IR Mixing on Isospectral Deformation Manifolds
• Twisted Covariance and Weyl Quantisation
• Quantum Field Theory on Noncommutative Space-Times and the Persistence of Ultraviolet Divergences
• The shuffle Hopf algebra and quasiplanar Wick products

Cited by in corpus (25)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Noncommutative field theories on $R_{\lambda }^3$: Towards UV/IR mixing freedom
• Noncommutative field theory from angular twist
• Noncommutative gauge theories on ${\mathbb{R}}_{\theta }^2$ as matrix models
• Curing the UV/IR mixing for field theories with translation-invariant $\star$ products
• Matrix Bases for Star Products: a Review
• $\kappa$-Minkowski star product in any dimension from symplectic realization
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Gauge and Poincare' Invariant Regularization and Hopf Symmetries
• Translational-invariant noncommutative gauge theory
• $\mathcal{P}\mathcal{T}$-symmetric quantum field theory on the noncommutative spacetime
• Extending general covariance: Moyal-type noncommutative manifolds
• Gauge Invariant Cutoff QED
• Consistent Anomalies in Translation-Invariant Noncommutative Gauge Theories
• Translation-Invariant Noncommutative Renormalization
• The Hierarchy Problem: From the Fundamentals to the Frontiers
• Perturbative effective action for the photon in noncommutative QED${}_2$ and exactness of the Schwinger mass
• Remarks on the interquark potential in the presence of a minimal length
• Commutative deformations of general relativity: nonlocality, causality, and dark matter
• alpha^star-Cohomology and Classification of Translation-Invariant Non-Commutative Quantum Field Theories
• star-Cohomology, Third Type Chern Character and Anomalies in General Translation-Invariant Noncommutative Yang-Mills
• On the UV/IR mixing of Lie algebra-type noncommutatitive ${\varphi }^4$-theories
• Green's Functions for Translation Invariant Star Products
• On Finite Noncommutativity in Quantum Field Theory
• Aspects of Group Field Theory