Multiplicity of self-adjoint realisations of the (2+1)-fermionic model of Ter-Martirosyan--Skornyakov type

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dc.contributor.areaMathematicsen_US
dc.contributor.authorMichelangeli, Alessandro
dc.contributor.authorOttolini, Andrea
dc.date.accessioned2017-01-16T12:25:32Z
dc.date.available2017-01-16T12:25:32Z
dc.date.issued2016-12
dc.description.abstractWe 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 Kreĭn, Višik, and Birman. We identify the explicit ‘Kreĭn-Višik–Birman extension parameter’ as an operator on the ‘space of charges’ for this model (the ‘Kreĭn 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.en_US
dc.identifier.urihttps://openscience.sissa.it/handle/1963/35267
dc.language.isoenen_US
dc.miur.area1en_US
dc.relation.ispartofseriesSISSA;65/2016/MATE
dc.subjectPoint interactionsen_US
dc.subjectSingular perturbations of the Laplacianen_US
dc.subjectSelf-adjoint ex- tensionsen_US
dc.subjectKreĭn-Višik-Birman theoryen_US
dc.subjectTer-Martirosyan{Skornyakov operatorsen_US
dc.subjectFermionic models of zero-range interactionsen_US
dc.titleMultiplicity of self-adjoint realisations of the (2+1)-fermionic model of Ter-Martirosyan--Skornyakov typeen_US
dc.typePreprinten_US
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