Non-commutative Field Theory, Translational Invariant Products and Ultraviolet/Infrared Mixing

TL;DR

This paper reviews translation-invariant non-commutative products like Moyal and Wick-Voros, applies them to phi^4 quantum field theories, and explores their connections with Drinfeld twists, focusing on one-loop Green's functions and UV/IR mixing.

Contribution

It provides a comprehensive review of non-commutative products and applies them to quantum field theory, including explicit calculations of Green's functions and analysis of UV/IR mixing.

Findings

Calculated one-loop Green's functions for phi^4 theories

Analyzed UV/IR mixing effects in non-commutative field theories

Explored connections with Drinfeld twists

Abstract

We review the Moyal and Wick-Voros products, and more in general the translation invariant non-commutative products, and apply them to classical and quantum field theory. We investigate phi^4 field theories calculating their Green's functions up to one-loop for the two- and four-point cases. We also review the connections of these theories with Drinfeld twists.