Non-relativistic Fermions, Coadjoint Orbits of \winf\ and String Field Theory at $c=1$

TL;DR

This paper develops a geometric formulation of non-relativistic fermions in one dimension using coadjoint orbits of \\winf-algebra, connecting quantum phase space, string theory, and classical fluid dynamics, with implications for strong coupling regimes.

Contribution

It introduces a novel geometric approach to non-relativistic fermions via coadjoint orbits of \\winf, linking quantum theory, string coupling, and classical fluid descriptions.

Findings

Leading order reduces to geometric action for classical fermi fluid

Method applicable to interacting fermions in one dimension

Strong coupling limit lacks a 2D space-time interpretation

Abstract

We apply the method of coadjoint orbits of \winf-algebra to the problem of non-relativistic fermions in one dimension. This leads to a geometric formulation of the quantum theory in terms of the quantum phase space distribution of the fermi fluid. The action has an infinite series expansion in the string coupling, which to leading order reduces to the previously discussed geometric action for the classical fermi fluid based on the group $w_\infty$ of area-preserving diffeomorphisms. We briefly discuss the strong coupling limit of the string theory which, unlike the weak coupling regime, does not seem to admit of a two dimensional space-time picture. Our methods are equally applicable to interacting fermions in one dimension.