Boson and Fermion Operator Realizations of Schur-Functions Appearing in Solvable Nonlinear Models

Abstract

Aggregate creation (or annihilation) operators of one-dimensional spinless bosons are found as operator realization of Schur-functions i.e. Young diagrams. A unitary operator is introduced to transform the aggregate boson operator into the fermion operator that also acts as an operator form of the Young diagram. The fermion operator produces, in case it acts on vacuum, the uncoupled fermion state just describable in Sato’s Maya diagram. Further, characteristic of S-function comes out in such quantum-mechanical solvable models, a boson model of the present author and a simplified Tomonaga-Luttinger model. Usefulness of the unitary operator is demonstrated also as a partial restatement of the theory of Kadomtsev-Petviashvili equation.