01319nas a2200109 4500008004100000245011100041210006900152520088700221100002901108700002101137856005101158 2016 en d00aMultiplicity of self-adjoint realisations of the (2+1)-fermionic model of Ter-Martirosyan--Skornyakov type0 aMultiplicity of selfadjoint realisations of the 21fermionic mode3 aWe 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,
Višiik, and Birman. We identify the explicit `Kreĭn-Višik-Birman extension param-
eter' 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 re-
produce for the first time the previous partial constructions obtained by means of
an alternative quadratic form approach.1 aMichelangeli, Alessandro1 aOttolini, Andrea uhttp://urania.sissa.it/xmlui/handle/1963/35267