Quantum inverse scattering method for the q-boson model and symmetric functions

Author: Tsilevich, N.¹

Source: Functional Analysis and Its Applications, Volume 40, Number 3, July 2006 , pp. 207-217(11)

Publisher: Springer

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Abstract:

The purpose of this paper is to show that the quantum inverse scattering method for the so-called q-boson model has a nice interpretation in terms of the algebra of symmetric functions. In particular, in the case of the phase model (corresponding to q = 0) the creation operator coincides (modulo a scalar factor) with the operator of multiplication by the generating function of complete homogeneous symmetric functions, and the wave functions are expressed via the Schur functions s_λ(x). The general case of the q-boson model is related in a similar way to the Hall-Littlewood symmetric functions P_λ(x;q²).

Keywords: q-boson model; phase model; quantum inverse scattering method; symmetric functions; Hall-Littlewood functions; Schur functions

Document Type: Research article

DOI: 10.1007/s10688-006-0032-1

Affiliations: 1: Email: natalia@pdmi.ras.ru

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