TY - RPRT
T1 - Multiplicity of self-adjoint realisations of the (2+1)-fermionic model of Ter-Martirosyan--Skornyakov type
Y1 - 2016
A1 - Alessandro Michelangeli
A1 - Andrea Ottolini
AB - 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 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.
UR - http://urania.sissa.it/xmlui/handle/1963/35267
U1 - 35573
U2 - Mathematics
U4 - 1
ER -