Noncommutative field theory from angular twist

TL;DR

This paper develops a noncommutative field theory based on angular noncommutativity, deriving the star-product from a twist operator, and analyzes its quantum properties and particle decay kinematics.

Contribution

It introduces a new noncommutative field theory framework using angular twist and explores its quantum behavior and particle decay processes.

Findings

The star-product is invariant under twisted Poincaré transformations.

One-loop analysis reveals UV/IR mixing in the theory.

Particle decay kinematics differ in space-only and space-time deformed scenarios.

Abstract

We consider a noncommutative field theory with space-time $\star$-commutators based on an angular noncommutativity, namely a solvable Lie algebra: the Euclidean in two dimension. The $\star$-product can be derived from a twist operator and it is shown to be invariant under twisted Poincar\'e transformations. In momentum space the noncommutativity manifests itself as a noncommutative $\star$-deformed sum for the momenta, which allows for an equivalent definition of the $\star$-product in terms of twisted convolution of plane waves. As an application, we analyze the $\lambda \phi^4$ field theory at one-loop and discuss its UV/IR behaviour. We also analyze the kinematics of particle decay for two different situations: the first one corresponds to a splitting of space-time where only space is deformed, whereas the second one entails a non-trivial $\star$-multiplication for the time variable, while one of the three spatial coordinates stays commutative.