The index of scattering operators of Dirac equations
type: Item
instance of: scholarly article
title: The index of scattering operators of Dirac equations
zbMATH Open document ID: 0636.58029
DOI: 10.1007/BF01205548
author: Taku Matsui
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: The author considers a quantized Dirac field on Minkowski-space, minimally coupled to an external gauge field with gauge group U(N). It is shown that, under some technical conditions, the index of the scattering operator: (i) vanishes in the massive case; (ii) equals the instanton number \((-1/8\pi^ 2)\int Tr(F\wedge F)\) in the massless case, where F denotes the curvature two form of the gauge field. The aforementioned conditions are such that the unitarity of S and the compactness of [P,S] are guaranteed (where \(S=scattering\) operator and \(P=projection\) onto the positive spectral subspace of the free Dirac operator).
Mathematics Subject Classification ID: 58J20
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 81T99
zbMATH DE Number: 4036769
zbMATH Keywords: quantized Dirac field
zbMATH Keywords: external gauge field
zbMATH Keywords: gauge group U(N)
zbMATH Keywords: index of the scattering operator
reviewed by: Volker Perlick
MaRDI profile type: Publication
cites work: Q4727695
cites work: Q3314566
cites work: Absence of vacuum polarisation in Fock space
cites work: Direct proof of the formula for the index of an elliptic system in Euclidean space
cites work: Q3736112
cites work: Q3785412
cites work: Scattering automorphisms of the Dirac field
cites work: Q5653193
cites work: Selected topics in gauge theories
cites work: The Chern classes of Sobolev connections
full work available at URL: https://doi.org/10.1007/bf01205548
OpenAlex ID: W2019268607
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description: scientific article; zbMATH DE number 4036769