Simple condensation of composite bosons in a number conserving approach to many fermion-systems

Abstract

We recently derived the Hamiltonian of fermionic composites by an exact procedure of bosonization. In the present paper expand this Hamiltonian in the inverse of the number of fermionic states in the composite wave function and give the necessary and sufficient conditions for the validity of such an expansion. We compare the results to the Random phase Approximation and the BCS theory and perform an illustrative application of the method. √nbKb † 0 and rewrite the Hamiltonian accordinglŷ

Diquarks in the nilpotency expansion of QCD and their role at finite chemical potential

“…If we make the Bogoliubov transformation time-dependent, we can conserve fermion number by the help of compensating fields. The development of this approach for many-body systems can be found in [48].…”

“…From the technical point of view our formalism is a fermion number conserving extension of the theory of superconductivity developed by Bogoliubov and Valatin [34,35] which violates this symmetry. The enforcement of fermion conservation in manybody theories can indeed be achieved by allowing time-dependence of the Bogolibov transformation [36]. In the saddle point approximation, however, one gets a formulation close to the quasi-chemical equilibrium theory of superconductors developed by the Sydney group [37], in which fermion number is explicitly preserved.…”