Exact bosonization for an interacting Fermi gas in arbitrary dimensions

TL;DR

This paper introduces an exact bosonization method for interacting fermions in any dimension, enabling new analytical and numerical approaches, including Monte Carlo simulations free from the sign problem.

Contribution

It provides a universal, exact mapping of interacting fermion models to bosonic models applicable in all dimensions and interactions, with potential for improved computational techniques.

Findings

Mapping is applicable in any dimension and for any interaction.

The bosonization may eliminate the sign problem in Monte Carlo simulations.

A new field theory based on superfields is derived for analytical studies.

Abstract

We present an exact mapping of models of interacting fermions onto boson models. The bosons correspond to collective excitations in the initial fermionic models. This bosonization is applicable in any dimension and for any interaction between fermions. We show schematically how the mapping can be used for Monte Carlo calculations and argue that it should be free from the sign problem. Introducing superfields we derive a field theory that may serve as a new way of analytical study.