Curing the UV/IR mixing for field theories with translation-invariant $\star$ products

Abstract

The ultraviolet/infrared (UV/IR) mixing of noncommutative field theories has been recently shown to be a generic feature of translation- invariant associative products. In this paper we propose to take into account the quantum corrections of the model to modify in this way the noncommutative action. This idea was already used to cure the UV/IR mixing for theories on Moyal space. We show that in the present framework also, this proposal proves successful for curing the mixing. We achieve this task by explicit calculations of one and higher loops Feynman amplitudes. For the sake of completeness, we compute the form of the new action in the matrix base for the Wick-Voros product.

21 pages, 7 figures; discussion for the Minkowskian case added; version accepted for publication in Phys. Rev. D

References in corpus (20)

• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Algebras of distributions suitable for phase-space quantum mechanics. I
• Voros product, Noncommutative Schwarzschild Black Hole and Corrected Area Law
• A translation-invariant renormalizable non-commutative scalar model
• Twisting all the way: from Classical Mechanics to Quantum Fields
• Vacuum configurations for renormalizable non-commutative scalar models
• Three Dimensional Quantum Geometry and Deformed Poincare Symmetry
• Twisted Noncommutative Field Theory with the Wick-Voros and Moyal Products
• Combinatorial Dyson-Schwinger equations in noncommutative field theory
• Non-Commutative Complete Mellin Representation for Feynman Amplitudes
• Commutative limit of a renormalizable noncommutative model
• Overview of the parametric representation of renormalizable non-commutative field theory
• Parametric representation of "critical" noncommutative QFT models
• Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing
• Parametric representation of a translation-invariant renormalizable noncommutative model
• Inequivalence of QFT's on Noncommutative Spacetimes: Moyal versus Wick-Voros
• Twisted Quantum Fields on Moyal and Wick-Voros Planes are Inequivalent
• One-loop $\beta$ functions of a translation-invariant renormalizable noncommutative scalar model
• Macroscopic Screening of Coulomb Potentials From UV/IR-Mixing
• Feynman amplitudes in renormalizable non-commutative quantum field theory

Cited by in corpus (16)

• Noncommutative field theory on ${\mathbb{R}}_{\lambda }^3$
• Combinatorial Hopf Algebras in (Noncommutative) Quantum Field Theory
• A unifying perspective on the Moyal and Voros products and their physical meanings
• On the $\star$-product quantization and the Duflo map in three dimensions
• Matrix Bases for Star Products: a Review
• Translational-invariant noncommutative gauge theory
• Gauge Invariant Cutoff QED
• The Gribov problem in Noncommutative gauge theory
• Translation-Invariant Noncommutative Renormalization
• T-Dualities and Doubled Geometry of the Principal Chiral Model
• Voros product and the Pauli principle at low energies
• Casimir energy for a spherical boundary within the surface impedance approach: Obtaining negative values
• Energy momentum tensor for translation invariant renormalizable noncommutative field theory
• alpha^star-Cohomology and Classification of Translation-Invariant Non-Commutative Quantum Field Theories
• Green's Functions for Translation Invariant Star Products
• star-Cohomology, Third Type Chern Character and Anomalies in General Translation-Invariant Noncommutative Yang-Mills