On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory

TL;DR

This paper reviews the harmonic term in noncommutative scalar field theory, explaining its role in renormalizability and exploring its interpretations through duality, superalgebra, and curvature perspectives.

Contribution

It clarifies the connections between different interpretations of the harmonic term, enhancing understanding of its fundamental role in noncommutative quantum field theory.

Findings

Harmonic term removes UV-IR mixing in scalar field theory

Deep relationships between duality, superalgebra, and curvature interpretations are established

The harmonic term ensures renormalizability of the theory

Abstract

The harmonic term in the scalar field theory on the Moyal space removes the UV-IR mixing, so that the theory is renormalizable to all orders. In this paper, we review the three principal interpretations of this harmonic term: the Langmann-Szabo duality, the superalgebraic approach and the noncommutative scalar curvature interpretation. Then, we show some deep relationship between these interpretations.