Infinitesimal spectral flow and scattering matrix

Details Infinitesimal spectral flow and scattering matrix Infinitesimal spectral flow and scattering matrix

2007-05-23

arxiv.org/abs/0705.3282v4

Mathematics

Spectral Theory

12 pages, LaTeX; minor changes

Scientific paper

In this note the notion of infinitesimal scattering matrix is introduced. It is shown that under certain assumption, the scattering operator of a pair of trace compatible operators is equal to the chronological exponential of the infinitesimal scattering matrix and that the trace of the infinitesimal scattering matrix is equal to the absolutely continuous part of the infinitesimal spectral flow. As a corollary, a variant of the Birman-Krein formula is derived. An interpretation of Pushnitski's $\mu$-invariant is given.

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