Study of the mathematical approximations made in the basis-correlation method and those made in the canonical-transformation method for an interacting Bose gas

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Abstract
Following up a new method for solving a many-body Bose gas proposed by Wong and Fung previously, we extend our study to summing all terms relating to the three-body correlation function in the canonical-transformation matrix representation. It was found that only a certain class of interaction potential will allow for an analytic representation of the one-to-one linear transformation matrices. However, the variational method based on construction of the basis correlations does not have such mathematical restriction.