Quadratic Forms for the Fermionic Unitary Gas Model
Abstract
We consider a quantum system in dimension three composed by a group of N identical fermions, with mass 1/2, interacting via zerorange interaction with a group of M identical fermions of a different type, with mass m/2. Exploiting a renormalization procedure, we construct the corresponding quadratic form and define the socalled SkornyakovTerMartirosyan extension H_{α}, which is the natural candidate as a possible Hamiltonian of the system. It is shown that if the form is unbounded from below then H_{α} is not a selfadjoint and bounded from below operator, and this in particular suggests that the socalled Thomas effect could occur. In the special case N = 2, M = 1 we prove that this is in fact the case when a suitable condition on the parameter m is satisfied.
 Publication:

Reports on Mathematical Physics
 Pub Date:
 April 2012
 DOI:
 10.1016/S00344877(12)600226
 Bibcode:
 2012RpMP...69..131F
 Keywords:

 zerorange interactions;
 unitary gas;
 SkornyakovTerMartirosyan extension