Noncommutative Cubic Scalar Field Theory and Tree Level Processes

TL;DR

This paper investigates how noncommutative deformations, via the Groenewald-Moyal product, modify tree-level scattering amplitudes in cubic scalar field theory, revealing nontrivial corrections and exploring position-dependent noncommutativity effects.

Contribution

It introduces a detailed analysis of noncommutative corrections to tree-level scattering in cubic scalar field theory, including the impact of localized noncommutativity parameters.

Findings

Noncommutative corrections alter 2->2 scattering amplitudes.

Tree-level scattering receives nontrivial modifications due to noncommutativity.

Position-dependent noncommutativity introduces new theoretical considerations.

Abstract

In this paper, we study the corrections to tree level scattering that arise due to noncommutative deformations of cubic scalar field theory through implementation of the Groenewald-Moyal(GM) product. The additional noncommutative refinement as we shall see, supplies nontrivial corrections to scattering even at the tree level. The amplitudes for 2 -> 2 scattering are computed and elucidated. Finally, we also consider the possibility of a localized noncommutativity parameter and the possible consequences of introducing position dependence in spacetime noncommutativity