Many-particle models with two constants of interaction
type: Item
instance of: scholarly article
title: Many-particle models with two constants of interaction
zbMATH Open document ID: 1085.81047
published in: Journal of Mathematical Sciences (New York)
publication date: 2006-01-23T00:00:00Z
review text: The author discusses integrable models of quantum field theory and statistical mechanics. The dynamics and kinematics of these models are defined by Hamiltonians with symmetries determined by Lie algebras. The paper is devoted to the characterization of models such that the root vectors of their symmetry algebras run two orbits under the action of the Weyl group. Such properties possess root systems of the type \(B_N\), \(C_N\) and \(G_2\). The main focus is on models with the symmetry of algebras \(B_N\). In this case the main characteristics of the process are obtained from the system of Yang-Baxter equation and the reflection equations. The author considers the Calogero-Moser and Calogero-Sutherland models and also the formalisms of the Lax and Dunkl operators. The connection between these formalisms and method of describing these models in terms of the generalized Knizhnik-Zamolodchikov equations with the system of roots of the type \(B_N\) by the example of the Gaudin model with reflection are discussed. Examples of many-particle systems that interact with each other with reflections are presented.
reviewed by: Marian Ioan Munteanu
Mathematics Subject Classification ID: 81R12
Mathematics Subject Classification ID: 81T10
Mathematics Subject Classification ID: 32G34
zbMATH DE Number: 5000622
zbMATH Keywords: quantum field theory
zbMATH Keywords: Yang-Baxter equation
zbMATH Keywords: reflection equation
zbMATH Keywords: integrable systems
author: Valentina Golubeva
MaRDI profile type: Publication
full work available at URL: s10958-005-0293-x
OpenAlex ID: W1980334601
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DOI: 10.1007/S10958-005-0293-X
description: scientific article; zbMATH DE number 5000622