Undetermined-constant method in the boson Green’s-function theory

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Abstract
It is shown in the present paper that if operators of a boson Green’s function involve arbitrary c numbers, then the corresponding correlation function obtained from the spectral theorem is independent of the c numbers, which is in contradiction with the definition of the said correlation function. In order to solve this problem we have introduced an undetermined-constant method and applied it to ferromagnetic and ferroelectric systems, respectively. It is pointed out that the introduction of the undetermined constant is an intrinsic characteristic of the boson Green’s-function method and that contradictory results can often be obtained if it is not introduced.