TL;DR
This paper reviews noncommutative quantum mechanics and field theories, focusing on the Moyal product, UV/IR mixing, and the renormalization of noncommutative models like the Wess-Zumino theory.
Contribution
It provides a detailed analysis of renormalizable noncommutative quantum field theories and discusses their low energy behavior and infrared singularities.
Findings
Identification of conditions for renormalizability in noncommutative QFTs
Analysis of UV/IR mixing effects in noncommutative models
Quantization and low energy analysis of the noncommutative Wess-Zumino model
Abstract
We start by reviewing the formulation of noncommutative quantum mechanics as a constrained system. Then, we address to the problem of field theories defined on a noncommutative space-time manifold. The Moyal product is introduced and the appearance of the UV/IR mechanism is exemplified. The emphasis is on finding and analyzing noncommutative quantum field theories which are renormalizable and free of nonintegrable infrared singularities. In this last connection we give a detailed discussion of the quantization of the noncommutative Wess-Zumino model as well as of its low energy behavior.
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