Connections and effective S-matrix in triangle representation for quantum scattering
type: Item
instance of: scholarly article
title: Connections and effective S-matrix in triangle representation for quantum scattering
zbMATH Open document ID: 0733.58042
DOI: 10.1016/0003-4916(91)90019-5
author: Yu. A. Kuperin
author: Pavel Kurasov
author: Yu. B. Mel'nikov
author: S. P. Merkur'ev
published in: Annals of Physics
publication date: 1991-01-01T00:00:00Z
full work available at URL: http://hdl.handle.net/11701/1679
review text: The author consider a quantum system on a Hilbert space of the form \({\mathfrak H}=L^ 2(M\times N,d{\hat \mu})\), where d\({\hat \mu}\) is some positive measure on \(M\times N\). This is equivalent to considering a Hilbert bundle with fibers of the form \(F_ x=L^ 2(N,dm_ x)\) over the base manifold M. For a special type of Hamiltonians H, the spectral problem \(H\psi =z\psi\) is discussed, in connection with the so-called triangle expansion for the eigenfunction \(\psi\). In this set-up, some relations between global invariants of the S-matrix and connections on the corresponding Hilbert bundle are found. In applications to few-body scattering problems the bundle structure is achieved by extracting certain sub-Hamiltonians.
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 81U20
Mathematics Subject Classification ID: 58J60
Mathematics Subject Classification ID: 58J90
zbMATH DE Number: 4213075
zbMATH Keywords: quantum system
zbMATH Keywords: spectral problem
zbMATH Keywords: triangle expansion
zbMATH Keywords: S-matrix
zbMATH Keywords: connections
zbMATH Keywords: Hilbert bundle
zbMATH Keywords: scattering problems
reviewed by: Volker Perlick
MaRDI profile type: Publication
OpenAlex ID: W2161914511
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description: scientific article; zbMATH DE number 4213075