Conserving and gapless approximations for the composite bosons in terms of the constituent fermions

Dipartimento di Fisica, Università di Camerino - I-62032 Camerino, Italy

Received: 10 February 2005
Accepted: 5 June 2005

Abstract

A well-known problem with the many-body approximations for interacting condensed bosons is the dichotomy between the “conserving” and “gapless” approximations, which either obey the conservations laws or satisfy the Hugenholtz-Pines condition for a gapless excitation spectrum, in the order. It is here shown that such a dichotomy does not exist for a system of composite bosons, which form as bound-fermion pairs in the strong-coupling limit of the fermionic attraction. By starting from the constituent fermions, for which conserving approximations can be constructed for any value of the mutual attraction according to the Baym-Kadanoff prescriptions, it is shown that these approximations also result into a gapless excitation spectrum for the boson-like propagators in the broken-symmetry phase.