Universal fermionization of bosons on permutative representations of the Cuntz algebra ${\cal O}_{2}$

TL;DR

This paper demonstrates a universal method to transform bosonic operators into fermionic ones within any permutative representation of the Cuntz algebra ${\

Contribution

It introduces a universal fermionization process for bosons on permutative representations of ${\cal O}_2$, applicable across various representations including Fock space.

Findings

Fermionization universally holds on any permutative representation of ${\cal O}_2$

Explicit fermionizations demonstrated on Fock space and infinite wedge

Provides a new algebraic framework for boson-fermion correspondence

Abstract

Bosons and fermions are described by using canonical generators of Cuntz algebras on any permutative representation. We show a fermionization of bosons which universally holds on any permutative representation of the Cuntz algebra ${\cal O}_{2}$. As examples, we show fermionizations on the Fock space and the infinite wedge.