How to bosonize fermions with non-linear energy dispersion

TL;DR

This paper introduces a systematic approach to incorporate non-linear energy dispersion effects into fermionic bosonization, explicitly calculating quadratic corrections and highlighting the importance of curvature in quantum Hall systems.

Contribution

It presents a novel method to account for non-linear dispersion in bosonization across dimensions, including explicit correction calculations and applications to quantum Hall curvature effects.

Findings

Quadratic energy dispersion corrections are explicitly derived.

Curvature effects are shown to be crucial in quantum Hall Chern-Simons theory.

The method generalizes bosonization to non-linear dispersions in arbitrary dimensions.

Abstract

We develop a systematic method to treat the effect of non-linearity in the energy dispersion on the usual bosonization result for the single-particle Green's function of fermions in arbitrary dimension. The leading corrections due to the quadratic term in the energy dispersion are explicitly calculated. In the Chern-Simons theory for half-filled quantum Hall systems curvature is shown to be essential.