Abstract
It is shown that the method of the two-time Green's function, in the first order approximation of the binary kernel, leads to the same type of divergence for the many-boson systems, as a divergence noticed for the case of the Heisenberg model. By introducing the “collision kernel” and collecting all the terms of the second order of the collision kernels, a convergent result is achieved. The result gives a justification for the manipulation which Morita and Tanaka proposed in order to obtain the Dyson's T 4 term for the Heisenberg ferromagnet.
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