Dimensional regularization and renormalization of non-commutative QFT

Abstract

Using the recently introduced parametric representation of non-commutative quantum field theory, we implement here the dimensional regularization and renormalization of the vulcanized ${\Phi }_4^{\star 4}$ model on the Moyal space.

31 pages, 8 figures

Cited by in corpus (13)

• Multi-orientable Group Field Theory
• Combinatorial Dyson-Schwinger equations in noncommutative field theory
• Commutative limit of a renormalizable noncommutative model
• Parametric representation of a translation-invariant renormalizable noncommutative model
• Curing the UV/IR mixing for field theories with translation-invariant $\star$ products
• Vanishing beta function for Grosse-Wulkenhaar model in a magnetic field
• Symmetries of noncommutative scalar field theory
• Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term ${\sum }_s|p_s|+\mu$
• One-loop $\beta$ functions of a translation-invariant renormalizable noncommutative scalar model
• On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
• Translation-Invariant Noncommutative Renormalization
• Renormalization of the commutative scalar theory with harmonic term to all orders
• The renormalization of non commutative ϕ_4^{\star 4}