Bosonization and Fermionization of the Superstring Oscillators

Abstract

In this manuscript we consider the transformations of the oscillators of the bosonic fields of the superstring in terms of the fermions oscillators and vice versa. We demand the exchange of the commutation and anti-commutation relations of the oscillators.Therefore, we obtain some conditions on the Grassmannian matrices that appear in these transformations. We observe that there are several methods to obtain these conditions. In addition, adjoints of the matrix elements and T -duality of these matrices will be obtained. The effects of this bosonization and fermionization on the mass operators and on some massless states will be studied. The covariant formalism will be used and hence we consider both the matter parts and the ghost parts of the superstring theory.

Universal fermionization of bosons on permutative representations of the Cuntz algebra O2

“…It is often said that bosons can be written by using fermions in various contexts [11,18,20]. Such a description is called a fermionization of bosons in the broad sense of the term.…”

“…At the last of this section, we consider the inverse formula of Theorem 1.4. When fermions are written by using bosons, such a description is called a bosonization of fermions in the broad sense of the term [5,11,16,21]. Theorem 1.4 brings the following natural question.…”