Normal modes of the d>1 fermion gas

TL;DR

This paper develops a method to solve the many-fermion problem in higher dimensions by decomposing the Fermi sea into independent sectors and identifying their normal modes, providing insights into bosonization, exchange, pairing, and quasiparticles.

Contribution

It introduces a novel approach to analyze many-fermion systems in dimensions greater than one by decomposing the Fermi sea into independent sectors and constructing exact eigenstates.

Findings

Exact eigenstates constructed from sector eigenstates

Insights into bosonization and pairing in higher dimensions

Framework applicable to complex many-fermion phenomena

Abstract

In the present work we solve the many-fermion problem in dimensions greater than one by identifying its normal modes. We start by decomposing the Fermi sea into independent sectors labeled by a wavevector q. The product of exactly calculable eigenstates, one from each sector, is an exact eigenstate of the full many-body problem. We examine bosonization of fermions, exchange and pairing forces and quasiparticles, all from this point of view.