Abstract
Bi-local mean field theory is applied to a one-dimensional quantum liquid with a long range 1/ r 2 interaction, which has an exact ground state wave function. We obtain a mean field solution and an effective action which expresses a long range dynamics. Based on them the ground state energy and correlation functions are computed. The ground state energy agrees fairly well with the exact value and the exponents have a weaker coupling constant dependence than that of the partly known exact value.
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