Quantum Corrections for Translation-Invariant Renormalizable Non-Commutative Phi^4 Theory

Abstract

In this paper we elaborate on the translation-invariant renormalizable Phi^4 theory in 4-dimensional non-commutative space which was recently introduced by the Orsay group. By explicitly performing Feynman graph calculations at one loop and higher orders we illustrate the mechanism which overcomes the UV/IR mixing problem and ultimately leads to a renormalizable model. The obtained results show that the IR divergences are also suppressed in the massless case, which is of importance for the gauge field theoretic generalization of the scalar field model.

18 pages, v2: slightly extended version including a new section on one-loop renormalization, v3: minor revision

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• Loop Calculations for the Non-Commutative U(1) Gauge Field Model with Oscillator Term
• On Non-Commutative U*(1) Gauge Models and Renormalizability
• Gauge Theories on Deformed Spaces
• The potential of large germanium detector arrays for solar-axion searches utilizing the axio-electric effect for detection
• Improved Localization of a Renormalizable Non-Commutative Translation Invariant U(1) Gauge Model
• Inferring the covariant $\Theta$-exact noncommutative coupling in the top quark pair production at linear colliders
• One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative 1/p**2 U(1) Gauge Model
• One loop radiative corrections to the translation-invariant noncommutative Yukawa Theory
• Gauge Fields on Non-Commutative Spaces and Renormalization
• Quantum Space-Time and Noncommutative Gauge Field Theories
• Translation-Invariant Renormalizable Noncommutative Chern-Simons Theory
• On NCQFT and dimensionless insertions