A new boson expansion theory utilizing a norm operator

Abstract We propose a new boson expansion method using norm operator. The small parameter expansion, in which the approximation becomes zeroth-order approximation, requires double commutation relations between phonon operators that are not closed excitation modes adopted as excitations. This results an infinite regardless of whether type is Hermitian or non-Hermitian. does hold when closed. operator expressed function number physical subspace, enables us to obtain substantially finite being also point out problems conventional methods. normal-ordered linked-cluster theory has failed refute Marshalek’s claim KT-1 and KT-2 chimerical expansions. Dyson have exceptional superiority over other types. Previous studies methods should be re-examined.