Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces

TL;DR

This paper provides an exact solution for a scalar quantum field theory on noncommutative phase spaces, analyzing Green's functions, scaling limits, and renormalizability, with an extension to supersymmetry.

Contribution

It offers the first exact solution of a noncommutative quantum field theory with explicit Green's functions and explores non-perturbative scaling limits and supersymmetric extensions.

Findings

Explicit Green's functions in arbitrary even dimensions

Non-perturbative analysis of scaling limits

Renormalizability properties of the model

Abstract

We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an interaction defined by the Groenewold-Moyal star-product. Explicit results are presented for all Green's functions in arbitrary even spacetime dimensionality. Various scaling limits of the field theory are analysed non-perturbatively and the renormalizability of each limit examined. A supersymmetric extension of the field theory is also constructed in which the supersymmetry transformations are parametrized by differential operators in an infinite-dimensional noncommutative algebra.