Linked-Pair Expansions in Quantum Statistics

Abstract

In the quantum statistical method of Lee and Yang, the cluster functions of quantum statistics are expressed in terms of the cluster functions of Boltzmann statistics, which in turn are computed in terms of certain two-body functions. In the present paper, following a detailed study of the Boltzmann cluster functions, it is shown that the symmetric representation can be used for the two-body functions and that large classes of diagrams can be summed. This leads to the introduction of linked-pair graphs to describe the functions of quantum statistics. The two-body functions are expressed in terms of two-body wave functions, and are therefore well-defined for hard-core repulsions. For weak potentials the method is shown to be equivalent to the theory of Bloch and DeDominicis.