Progress in solving a noncommutative quantum field theory in four dimensions

Abstract

We study the noncommutative ϕ^4_4-quantum field theory at the self-duality point. This model is renormalisable to all orders as shown in earlier work of us and does not have a Landau ghost problem. Using the Ward identity of Disertori, Gurau, Magnen and Rivasseau, we obtain from the Schwinger-Dyson equation a non-linear integral equation for the renormalised two-point function alone. The non-trivial renormalised four-point function fulfils a linear integral equation with the inhomogeneity determined by the two-point function. These integral equations are the starting point for a perturbative solution. In this way, the renormalised correlation functions are directly obtained, without Feynman graph computation and further renormalisation steps

15 pages, LaTeX with xy-pic

References in corpus (8)

• Noncommutative Perturbative Dynamics
• Hopf Algebras, Renormalization and Noncommutative Geometry
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Duality in Scalar Field Theory on Noncommutative Phase Spaces
• 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
• Non-commutative Renormalization
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory

Cited by in corpus (28)

• The Tensor Track, III
• Invitation to Random Tensors
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• Constructive Tensor Field Theory: The $T_3^4$ Model
• Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
• Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures
• Spectral geometry of the Moyal plane with harmonic propagation
• Solvable 4D noncommutative QFT: phase transitions and quest for reflection positivity
• Solution of all quartic matrix models
• Solvable limits of a 4D noncommutative QFT
• Exact solution of matricial ${\Phi }_2^3$ quantum field theory
• From scalar fields on quantum spaces to blobbed topological recursion
• Constructive Renormalization for ${\Phi }_2^4$ Theory with Loop Vertex Expansion
• Perturbative and Geometric Analysis of the Quartic Kontsevich Model
• An algebraic approach to a quartic analogue of the Kontsevich model
• Lehmann-Symanzik-Zimmermann S-Matrix elements on the Moyal Plane
• Nested Catalan tables and a recurrence relation in noncommutative quantum field theory
• High energy improved scalar quantum field theory from noncommutative geometry without UV/IR-mixing
• Matrix Field Theory
• Intermediate Field Representation for Positive Matrix and Tensor Interactions
• Aspects of quantum gravity
• The Multiscale Loop Vertex Expansion
• On the fixed point equation of a solvable 4D QFT model
• Constructive Renormalization of the 2-dimensional Grosse-Wulkenhaar Model with Multiscale Loop Vertex Expansions
• Wick rotation for quantum field theories on degenerate Moyal space(-time)
• Genus one free energy contribution to the quartic Kontsevich model