Planar limit of 1D many-body system

TL;DR

This paper reviews the classical limit of 1D many-body systems using matrix, collective field, and phase space theories, demonstrating exact solutions for large particle numbers, exemplified by bosonic and fermionic systems with delta interactions.

Contribution

It introduces a comprehensive review of classical descriptions of 1D many-body systems and provides exact solutions in the large particle number limit.

Findings

Classical descriptions simplify analysis of 1D systems in the planar limit.

Exact solutions are obtained for bosonic and fermionic systems with delta interactions.

Theories become classical and solvable as particle number approaches infinity.

Abstract

We review one dimensional matrix theory and its variations, collective field theory and quantum phase space description. In the planar limit, these theories become classical and can be easily analyzed. With these descriptions, one dimensional interacting many-body system can be solved exactly when the particle number goes to infinity. As an example, bosonic and two-component fermionic systems with a $\delta$-function interaction are analyzed in detail.