Integrable many-body problems in more than one dimension
type: Item
instance of: scholarly article
title: Integrable many-body problems in more than one dimension
zbMATH Open document ID: 0637.70007
DOI: 10.1016/0034-4877(86)90048-0
published in: Reports on Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: Integrable many-body problems in more than one dimension can be trivially constructed by piecing together one-dimensional integrable models. For instance the three-dimensional n-body problems with the Hamiltonian \[ H=1/2\sum^{n}_{j=1}(p^ 2_ j+\omega^ 2r^ 2_ j)+g^ 2\sum^{n}_{j>k=1}V(r_ j-r_ k) \] and the pair potentials \[ V(r)=(1-\sin^ 2\phi \sin^ 22\theta)/(r \cos \phi \cos 2\theta)^ 2 \] or \[ V(r)=(1-\sin^ 2\phi \cos^ 22\theta)/(r \sin 2\phi \sin 2\theta)^ 2 \] are integrable (here r, \(\theta\) and \(\phi\) are of course the polar coordinates of the 3-vector r).
Mathematics Subject Classification ID: 70F10
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 4039368
zbMATH Keywords: Integrable many-body problems
zbMATH Keywords: one-dimensional integrable models
zbMATH Keywords: three- dimensional n-body problems
author: Francesco Calogero
MaRDI profile type: Publication
full work available at URL: 0034-4877(86)90048-0
OpenAlex ID: W1968267984
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description: scientific article; zbMATH DE number 4039368