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Funktsional. Anal. i Prilozhen., 2006, Volume 40, Issue 3, Pages 53–65 (Mi faa743)  

This article is cited in 37 scientific papers (total in 37 papers)

Quantum Inverse Scattering Method for the $q$-Boson Model and Symmetric Functions

N. V. Tsilevich

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

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 $s_\lambda(x)$. The general case of the $q$-boson model is related in a similar way to the Hall–Littlewood symmetric functions $P_\lambda(x;q^2)$.

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

DOI: https://doi.org/10.4213/faa743

Full text: PDF file (239 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2006, 40:3, 207–217

Bibliographic databases:

UDC: 517.958
Received: 10.08.2005

Citation: N. V. Tsilevich, “Quantum Inverse Scattering Method for the $q$-Boson Model and Symmetric Functions”, Funktsional. Anal. i Prilozhen., 40:3 (2006), 53–65; Funct. Anal. Appl., 40:3 (2006), 207–217

Citation in format AMSBIB
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    This publication is cited in the following articles:
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  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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