Connections and effective S-matrix in triangle representation for quantum scattering
The author consider a quantum system on a Hilbert space of the form \({\mathfrak H}=L^ 2(M\times N,d{\hat \mu})\), where d\({\hat \mu}\) is some positive measure on \(M\times N\). This is equivalent to considering a Hilbert bundle with fibers of the form \(F_ x=L^ 2(N,dm_ x)\) over the base manifold M. For a special type of Hamiltonians H, the spectral problem \(H\psi =z\psi\) is discussed, in connection with the so-called triangle expansion for the eigenfunction \(\psi\). In this set-up, some relations between global invariants of the S-matrix and connections on the corresponding Hilbert bundle are found. In applications to few-body scattering problems the bundle structure is achieved by extracting certain sub-Hamiltonians.
scientific article; zbMATH DE number 4213075
scientific article