Bosonic realization of algebras in the Calogero model

TL;DR

This paper develops a bosonic realization of the nonlinear symmetry algebra in the Calogero model, providing a new algebraic framework for understanding its degenerate energy levels.

Contribution

It introduces a novel algebra of symmetric operators and maps it onto the Heisenberg algebra to analyze the Calogero model.

Findings

Constructed a new algebra of symmetric operators.

Mapped the algebra onto the Heisenberg algebra.

Provided a bosonic realization of the symmetry algebra.

Abstract

We study an N-body Calogero model in the S_N-symmetric subspace of the positive definite Fock space. We construct a new algebra of S_N-symmetric operators represented on the symmetric Fock space, and find a natural orthogonal basis by mapping the algebra onto the Heisenberg algebra. Our main result is the bosonic realization of nonlinear symmetry algebra describing the structure of degenerate levels of Calogero model.