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

TL;DR

This paper develops a number-conserving bosonization approach to describe composite bosons in many-fermion systems, expanding the Hamiltonian in inverse fermionic state number and comparing it to established theories.

Contribution

It introduces a systematic expansion of the composite boson Hamiltonian in the inverse of the fermionic state number, providing conditions for its validity and connecting it with RPA and BCS theories.

Findings

Derived conditions for the validity of the expansion.

Compared the approach to RPA and BCS theories.

Provided an illustrative application of the method.

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.