Exact Solution of Noncommutative Field Theory in Background Magnetic Fields

TL;DR

This paper presents an exact non-perturbative solution for a scalar field theory on a noncommutative space with background magnetic fields, revealing insights into non-local interactions and potential renormalizable models.

Contribution

It provides the first exact solution of a noncommutative scalar field theory in a magnetic background, highlighting its solvability with a finite ultraviolet cutoff.

Findings

Exact non-perturbative solution obtained

Model describes non-locally interacting charged particles

Perturbations may lead to renormalizable models

Abstract

We obtain the exact non-perturbative solution of a scalar field theory defined on a space with noncommuting position and momentum coordinates. The model describes non-locally interacting charged particles in a background magnetic field. It is an exactly solvable quantum field theory which has non-trivial interactions only when it is defined with a finite ultraviolet cutoff. We propose that small perturbations of this theory can produce solvable models with renormalizable interactions.