Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8256679 | Reports on Mathematical Physics | 2018 | 38 Pages |
Abstract
We reconstruct the whole family of self-adjoint Hamiltonians of Ter-Martirosyan-Skornyakov type for a system of two identical fermions coupled with a third particle of different nature through an interaction of zero range. We proceed through an operator-theoretic approach based on the self-adjoint extension theory of Krein, Višik, and Birman. We identify the explicit 'Krein-Višik-Birman extension parameter' as an operator on the 'space of charges' for this model (the 'Krein space') and we come to formulate a sharp conjecture on the dimensionality of its kernel. Based on our conjecture, for which we also discuss an amount of evidence, we explain the emergence of a multiplicity of extensions in a suitable regime of masses and we reproduce for the first time the previous partial constructions obtained by means of an alternative quadratic form approach.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Alessandro Michelangeli, Andrea Ottolini,