Noncommutative Field Theories and Smooth Commutative Limits

TL;DR

This paper investigates two noncommutative field theories with smooth limits to commutative theories, calculating bound states and scattering amplitudes to understand their behavior and differences from classical counterparts.

Contribution

It provides exact computations of bound state energies and scattering amplitudes for two specific noncommutative models with smooth commutative limits, highlighting their unique features.

Findings

Bound state energies computed exactly

Two-particle scattering amplitudes derived explicitly

Models exhibit smooth transition to commutative theories

Abstract

We consider two model field theories on a noncommutative plane that have smooth commutative limits. One is the single-component fermion theory with quartic interaction that vanishes identically in the commutative limit. The other is a scalar-fermion theory, which extends the scalar field theory with quartic interaction by adding a fermion. We compute the bound state energies and the two particle scattering amplitudes exactly.