Multiplicity of self-adjoint realisations of the (2+1)-fermionic model of Ter-Martirosyan—Skornyakov type
| Autor: | Alessandro Michelangeli, Andrea Ottolini |
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| Rok vydání: | 2018 |
| Předmět: |
Conjecture
Operator (physics) 010102 general mathematics Statistical and Nonlinear Physics Mathematics::Spectral Theory Type (model theory) Space (mathematics) 01 natural sciences Kernel (algebra) Quadratic form 0103 physical sciences 010307 mathematical physics 0101 mathematics Mathematical Physics Self-adjoint operator Curse of dimensionality Mathematics Mathematical physics |
| Zdroj: | Reports on Mathematical Physics. 81:1-38 |
| ISSN: | 0034-4877 |
| DOI: | 10.1016/s0034-4877(18)30014-4 |
| Popis: | 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, Visik, and Birman. We identify the explicit ‘Krein—Visik-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. |
| Databáze: | OpenAIRE |
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