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Relative index theorems and supersymmetric scattering theory

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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 theL 2-Euler characteristic.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-1000, Berlin 33, Federal Republic of Germany

    N. V. Borisov, W. Müller & R. Schrader

  2. Institut für Theorie der Elementarteilchen, Freie Universität Berlin, D-1000, Berlin, FRG

    N. V. Borisov & R. Schrader

  3. Karl-Weierstrass-Institut für Mathematik, Akademie der Wissenschaften der DDR, Berlin, German Democratic Republic

    W. Müller

Authors
  1. N. V. Borisov
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  2. W. Müller
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  3. R. Schrader
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Communicated by C. H. Taubes

On leave of absence from Institute of Physics, Leningrad State University, Leningrad

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Borisov, N.V., Müller, W. & Schrader, R. Relative index theorems and supersymmetric scattering theory. Commun.Math. Phys. 114, 475–513 (1988). https://doi.org/10.1007/BF01242140

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  • DOI: https://doi.org/10.1007/BF01242140

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