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math-phDec 14, 2007
22
citations (OpenAlex)
authors
  • Johannes Kellendonk
  • Serge Richard
institutions
  • Centre National de la Recherche Scientifique
  • Institut Camille Jordan
  • Lyon 1 Université
arXiv abstractPDF
paper

The topological meaning of Levinson's theorem, half-bound states included

arXiv:0712.2339 · doi:10.1088/1751-8113/41/29/295207

Abstract

We propose to interpret Levinson's theorem as an index theorem. This exhibits its topological nature. It furthermore leads to a more coherent explanation of the corrections due to resonances at thresholds.

arXiv comment4 pages

References in corpus (2)

  • Levinson's theorem for Schroedinger operators with point interaction: a topological approach
  • Topological boundary maps in physics: General theory and applications

Cited by in corpus (11)

  • Scattering theory for lattice operators in dimension d≥3
  • On the structure of the wave operators in one dimensional potential scattering
  • On the wave operators for the Friedrichs-Faddeev model
  • Levinson's theorem and higher degree traces for Aharonov-Bohm operators
  • On the wave operators and Levinson's theorem for potential scattering in R^3
  • Dimensional reduction and scattering formulation for even topological invariants
  • Does Levinson's theorem count complex eigenvalues ?
  • Impurity entropy of junctions of multiple quantum wires
  • Scattering approach for calculating one-loop effective action and vacuum energy
  • New formulae for the Aharonov-Bohm wave operators
  • Scattering theory and an index theorem on the radial part of SL(2,R)
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