Relative index theorems and supersymmetric scattering theory

N. V. Borisov, W. Müller, R. Schrader

Research output

42 Citations (Scopus)

Abstract

We discuss supersymmetric scattering theory and employ Krein's theory of spectral shift functions to investigate supersymmetric scattering systems. This is the basis for the derivation of relative index theorems on some classes of open manifolds. As an example we discuss the de Rham complex for obstacles in ℝN and asymptotically flat manifolds. It is shown that the absolute or relative Euler characteristic of an obstacle in ℝN may be obtained from scattering data for the Laplace operator on forms with absolute or relative boundary conditions respectively. In the case of asymptotically flat manifolds we obtain the Chern-Gauss-Bonnet theorem for the L2-Euler characteristic.

Original languageEnglish
Pages (from-to)475-513
Number of pages39
JournalCommunications in Mathematical Physics
Volume114
Issue number3
DOIs
Publication statusPublished - 1 Sep 1988

Fingerprint

Flat Manifold
Index Theorem
Scattering Theory
Euler Characteristic
theorems
Scattering
Spectral Shift Function
Laplace Operator
scattering
Gauss
Laplace transformation
Boundary conditions
derivation
Theorem
boundary conditions
shift
Form
Class

Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Borisov, N. V. ; Müller, W. ; Schrader, R. / Relative index theorems and supersymmetric scattering theory. In: Communications in Mathematical Physics. 1988 ; Vol. 114, No. 3. pp. 475-513.
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Relative index theorems and supersymmetric scattering theory. / Borisov, N. V.; Müller, W.; Schrader, R.

In: Communications in Mathematical Physics, Vol. 114, No. 3, 01.09.1988, p. 475-513.

Research output

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