Bosonization of current-current interactions

TL;DR

This paper extends bosonization techniques to current-current interactions using geometric quantization, illustrating with the Calogero-Sutherland model and gauge interactions, and analyzing fermion Green functions.

Contribution

It introduces a generalized bosonization method based on geometric quantization of $W_ olinebreak_\infty$ symmetries for current interactions, including nonintegrable cases.

Findings

Calogero-Sutherland model exemplifies the symmetry realization.

Fermion Green function computed for gauge interactions.

Provides a framework for bosonization beyond density operators.

Abstract

We discuss a generalization of the conventional bosonization procedure to the case of current-current interactions which get their natural representation in terms of current instead of fermion number density operators. A consistent bosonization procedure requires a geometrical quantization of the hamiltonian action of $W_\infty$ on its coadjoint orbits. An integrable example of a nontrivial realization of this symmetry is presented by the Calogero-Sutherland model. For an illustrative nonintegrable example we consider transverse gauge interactions and calculate the fermion Green function.