Twisted Noncommutative Field Theory with the Wick-Voros and Moyal Products

Abstract

We present a comparison of the noncommutative field theories built using two different star products: Moyal and Wick-Voros (or normally ordered). For the latter we discuss both the classical and the quantum field theory in the quartic potential case, and calculate the Green's functions up to one loop, for the two and four points cases. We compare the two theories in the context of the noncommutative geometry determined by a Drinfeld twist, and the comparison is made at the level of Green's functions and S-matrix. We find that while the Green's functions are different for the two theories, the S-matrix is the same in both cases, and is different from the commutative case.

arXiv commentThis is the merging of two previous postings: arXiv:0807.1492 and arXiv:0807.1498

References in corpus (39)

• String Theory and Noncommutative Geometry
• Deformation quantization of Poisson manifolds, I
• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• The quantum structure of spacetime at the Planck scale and quantum fields
• Noncommutative Perturbative Dynamics
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• A Gravity Theory on Noncommutative Spaces
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• An Introduction to Noncommutative Spaces and their Geometry
• Noncommutative Geometry and Gravity
• On the unitarity problem in space/time noncommutative theories
• Spin and Statistics on the Groenewold-Moyal Plane: Pauli-Forbidden Levels and Transitions
• Untwisting Noncommutative R^d and the Equivalence of Quantum Field Theories
• Moyal Planes are Spectral Triples
• Dynamics with Infinitely Many Derivatives: The Initial Value Problem
• Coherent State Induced Star-Product on $R_{\lambda }^3$ and the Fuzzy Sphere
• Deformed Coordinate Spaces; Derivatives
• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• Twisting all the way: from Classical Mechanics to Quantum Fields
• Generalized Coherent State Approach to Star Products and Applications to the Fuzzy Sphere
• UV-IR Mixing in Non-Commutative Plane
• Infinitely many star products to play with
• Twist Symmetry and Gauge Invariance
• Geometrical Evaluation of Star Products
• Spacetime and Fields, a Quantum Texture
• Twist and Spin-Statistics Relation in Noncommutative Quantum Field Theory
• Remarks on twisted noncommutative quantum field theory
• Twist to close
• Identical Particles and Quantum Symmetries
• Noncommutative spacetime symmetries: Twist versus covariance
• Noncommutative Field Theory from twisted Fock space
• Noncommutative Symmetries and Gravity
• A Fedosov Star Product of Wick Type for Kähler Manifolds
• Noncommutative Quantum Field Theory: A Confrontation of Symmetries
• Can QFT on Moyal-Weyl spaces look as on commutative ones?
• Statistics and Quantum Group Symmetries
• Why Renormalizable NonCommutative Quantum Field Theories?
• Quantum Field Theory on Noncommutative Space-Times and the Persistence of Ultraviolet Divergences

Cited by in corpus (41)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Voros product, Noncommutative Schwarzschild Black Hole and Corrected Area Law
• Noncommutative field theory from angular twist
• Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing
• Noncommutative Field Theory: Numerical Analysis with the Fuzzy Disc
• A unifying perspective on the Moyal and Voros products and their physical meanings
• Inequivalence of QFT's on Noncommutative Spacetimes: Moyal versus Wick-Voros
• On the $\star$-product quantization and the Duflo map in three dimensions
• Missing the point in noncommutative geometry
• Spinors and Voros star-product for Group Field Theory: First Contact
• Matrix Bases for Star Products: a Review
• Curing the UV/IR mixing for field theories with translation-invariant $\star$ products
• Twisted Quantum Fields on Moyal and Wick-Voros Planes are Inequivalent
• Finite axionic electrodynamics from a new noncommutative approach
• $\kappa$-Minkowski star product in any dimension from symplectic realization
• Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology
• Connecting dissipation and noncommutativity: A Bateman system case study
• Non-commutative Quantum Mechanics in Three Dimensions and Rotational Symmetry
• Algebras with convergent star products and their representations in Hilbert spaces
• Twist Deformation of Rotationally Invariant Quantum Mechanics
• Aspects of finite electrodynamics in D=3 dimensions
• Involutive representations of coordinate algebras and quantum spaces
• Gauge and Poincare' Invariant Regularization and Hopf Symmetries
• Spectral Properties and Local Density of States of Disordered Quantum Hall Systems with Rashba Spin-Orbit Coupling
• $\mathcal{P}\mathcal{T}$-symmetric quantum field theory on the noncommutative spacetime
• Translational-invariant noncommutative gauge theory
• Voros product, noncommutative inspired Reissner-Nordstr{ö}m black hole and corrected area law
• Noncommutative deformations of quantum field theories, locality, and causality
• The Gribov problem in Noncommutative gauge theory
• Translation-Invariant Noncommutative Renormalization
• A General formulation of the Moyal and Voros products and its physical interpretation
• Voros product and the Pauli principle at low energies
• Asymptotic commutativity of quantized spaces: the case of ${\mathbb{CP}}^{p,q}$
• Gribov horizon in Noncommutative QED
• Angles in Fuzzy Disc and Angular Noncommutative Solitons
• Noncommutative Conformal Field Theory in the Twist-deformed context
• Remarks on the interquark potential in the presence of a minimal length
• Quantum spaces, central extensions of Lie groups and related quantum field theories
• The Structure of Spacetime and Noncommutative Geometry
• Green's Functions for Translation Invariant Star Products
• Review of Twisted Poincare Symmetry