Bosonization in higher dimensions via noncommutative field theory

TL;DR

This paper introduces a novel bosonization method for many-body fermion systems in higher dimensions using noncommutative field theory, successfully reproducing key fermionic properties and demonstrated on a 2D fermion gas.

Contribution

It presents a new approach to bosonization in higher dimensions via noncommutative field theory, extending previous lower-dimensional techniques.

Findings

Reproduces fermionic Hilbert space and excitation energies

Demonstrates validity with 2D fermion gas in a harmonic trap

Establishes a chiral current algebra on noncommutative space

Abstract

We propose the bosonization of a many-body fermion theory in D spatial dimensions through a noncommutative field theory on a (2D-1)-dimensional space. This theory leads to a chiral current algebra over the noncommutative space and reproduces the correct perturbative Hilbert space and excitation energies for the fermions. The validity of the method is demonstrated by bosonizing a two-dimensional gas of fermions in a harmonic trap.