Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces

Abstract

We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an interaction defined by the Groenewold-Moyal star-product. Explicit results are presented for all Green's functions in arbitrary even spacetime dimensionality. Various scaling limits of the field theory are analysed non-perturbatively and the renormalizability of each limit examined. A supersymmetric extension of the field theory is also constructed in which the supersymmetry transformations are parametrized by differential operators in an infinite-dimensional noncommutative algebra.

70 pages AMSTeX

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Cited by in corpus (71)

• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Renormalisation of ϕ^4-theory on noncommutative R^2 in the matrix base
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Noncommutative Induced Gauge Theory
• The β-function in duality-covariant noncommutative ϕ^4-theory
• Renormalization of Non-Commutative Phi^4_4 Field Theory in x Space
• Renormalization of noncommutative phi 4-theory by multi-scale analysis
• Non-commutative Renormalization
• A translation-invariant renormalizable non-commutative scalar model
• Topics in Noncommutative Geometry Inspired Physics
• Vacuum configurations for renormalizable non-commutative scalar models
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory
• Renormalisation of ϕ^4-theory on noncommutative R^4 to all orders
• Parametric Representation of Noncommutative Field Theory
• Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
• Self-dual noncommutative ϕ^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory
• Magnetic Backgrounds and Noncommutative Field Theory
• On the vacuum states for noncommutative gauge theory
• Renormalization of the noncommutative phi^3 model through the Kontsevich model
• 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory
• Superintegrability of Kontsevich matrix model
• Overview of the parametric representation of renormalizable non-commutative field theory
• Parametric representation of "critical" noncommutative QFT models
• Noncommutative epsilon-graded connections
• Noncommutative geometry, gauge theory and renormalization
• Gauge theories on quantum spaces
• Noncommutative gauge theories on ${\mathbb{R}}_{\theta }^2$ as matrix models
• Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures
• Lectures on Matrix Field Theory I
• Exact Partition Functions for Gauge Theories on ${\mathbb{R}}_{\lambda }^3$
• Duality covariant quantum field theory on noncommutative Minkowski space
• Noncommutative gauge theories on ${\mathbb{R}}_{\lambda }^3$: Perturbatively finite models
• One-loop Beta Functions for the Orientable Non-commutative Gross-Neveu Model
• Closed star product on noncommutative ${\mathbb{R}}^3$ and scalar field dynamics
• Vanishing beta function for Grosse-Wulkenhaar model in a magnetic field
• A nontrivial solvable noncommutative ϕ^3 model in 4 dimensions
• Classical Solutions of the TEK Model and Noncommutative Instantons in Two Dimensions
• On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
• Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 1. Perturbative Expansion
• Duality and Braiding in Twisted Quantum Field Theory
• Deformed conformal and super-Poincaré symmetries in the non-(anti)commutative spaces
• Probing Noncommutativities of Phase Space by Using Persistent Charged Current and Its Asymmetry
• Divergences in quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential
• Extending general covariance: Moyal-type noncommutative manifolds
• Derivations of the Moyal Algebra and Noncommutative Gauge Theories
• Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 2. 1/θExpansion
• Constrains of Charge-to-Mass Ratios on Noncommutative Phase Space
• A Laplacian to compute intersection numbers on ${\bar{\mathcal{M}}}_{g,n}$ and correlation functions in NCQFT
• A Review of Noncommutative Field Theories
• UV/IR duality in noncommutative quantum field theory
• Isometric Embeddings and Noncommutative Branes in Homogeneous Gravitational Waves
• Complete solution of the LSZ Model via Topological Recursion
• Propagators and Matrix Basis on Noncommutative Minkowski Space
• The fate of the Wilson-Fisher fixed point in non-commutative ϕ^4
• Translation-Invariant Noncommutative Renormalization
• Matrix Model Fixed Point of Noncommutative Phi-Four
• Why Renormalizable NonCommutative Quantum Field Theories?
• Non-Commutative (Softly Broken) Supersymmetric Yang-Mills-Chern-Simons
• Constructive Renormalization of the $2$-dimensional Grosse-Wulkenhaar Model
• $U(N)$ Yang-Mills in non-commutative space time
• Noncommutative 3-colour scalar quantum field theory model in 2D
• Matrix Quantum Mechanics and Soliton Regularization of Noncommutative Field Theory
• Renormalization of the commutative scalar theory with harmonic term to all orders
• Complex (super)-matrix models with external sources and $q$-ensembles of Chern-Simons and ABJ(M) type
• Wilson RG of Noncommutative ${\Phi }_4^4$
• D-Branes in Noncommutative Field Theory
• Nonperturbative evaluation of the partition function for the real scalar quartic QFT on the Moyal plane at weak coupling
• Instantons, Fluxons and Open Gauge String Theory
• Partition function methods for the quartic scalar quantum field theory on the Moyal plane
• Constructive Renormalization of the 2-dimensional Grosse-Wulkenhaar Model with Multiscale Loop Vertex Expansions
• Noncommutative real scalar field theory in 2+1 dimensions at finite temperature