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1998•Journal of the Physical Society of JapanRequires access

Fock Spaces for the Calogero Models with Distinguishable Particles

Hideaki Ujino, Akinori Nishino, Miki Wadati

Open publisher page 12 citations

Abstract

We present the creation, annihilation and number operators for the A N -1 - and B N -Calogero models with distinguishable particles. In a parallel way to the construction of the Fock space of the quantum harmonic oscillators, we construct the Fock spaces as the simultaneous eigenfunctions of the number operators for the Calogero models. Relationships between the Fock spaces and the known nonsymmetric orthogonal bases, which are spanned by the variants of the Jack polynomials, are presented.

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What this paper is about

We present the creation, annihilation and number operators for the A N -1 - and B N -Calogero models with distinguishable particles. In a parallel way to the construction of the Fock space of the quantum harmonic oscillators, we construct the Fock spaces as the simultaneous eigenfunctions of the number operators for the Calogero models. Relationships between the Fock spaces and the known nonsymmetric orthogonal bases, which are spanned by the variants of the Jack polynomials, are presented.

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Available abstract

We present the creation, annihilation and number operators for the A N -1 - and B N -Calogero models with distinguishable particles. In a parallel way to the construction of the Fock space of the quantum harmonic oscillators, we construct the Fock spaces as the simultaneous eigenfunctions of the number operators for the Calogero models. Relationships between the Fock spaces and the known nonsymmetric orthogonal bases, which are spanned by the variants of the Jack polynomials, are presented.

Key concepts: Fock space, Creation and annihilation operators, Eigenfunction, Fock state, Physics, Space (punctuation), Annihilation, Quantum mechanics

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