Scattering theory by Enss' method for operator valued matrices: Dirac operator in an electric field
type: Item
instance of: scholarly article
title: Scattering theory by Enss' method for operator valued matrices: Dirac operator in an electric field
zbMATH Open document ID: 0581.47006
author: Pl. Muthuramalingam
published in: Journal of the Mathematical Society of Japan
publication date: 1985-01-01T00:00:00Z
review text: Existence of the modified wave operators and asymptotic completeness using Enss' method are proved for the operator \(H=H_ 0(P)+W_ S(Q,P)+W_ L(Q,P)I_ m\) on \([L^ 2(R^ n)]^ m\) where (i) \(H_ 0\) is a smooth map on \(R^ n\) taking values in the space of \(m\times m\) Hermitian matrices such that \(\lim_{| \zeta | \to \infty}| \lambda (\zeta)| =\infty\) for each eigenvalue \(\lambda\) (\(\zeta)\) of \(H_ 0(\zeta),\) (ii) \(W_ S(Q,P)\) is a short range pseudo differential operator on \([L^ 2(R^ n)]^ m,\) (iii) \(I_ m\) is the identity \(m\times m\) matrix and (iv) \(W_ L(Q,P)\) is a smooth long range pseudo differential operator on \(L^ 2(R^ n).\) The model includes the Dirac operator on \([L^ 2(R^ 3)]^ 4\) with an electric field.
Mathematics Subject Classification ID: 47A40
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 47L05
Mathematics Subject Classification ID: 46N99
zbMATH DE Number: 3929748
zbMATH Keywords: modified wave operators
zbMATH Keywords: asymptotic completeness
zbMATH Keywords: Enss' method
zbMATH Keywords: short range pseudo differential operator
zbMATH Keywords: Dirac operator
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/03730415
OpenAlex ID: W2025976088
DOI: 10.2969/JMSJ/03730415
description: scientific article; zbMATH DE number 3929748