Wigner-distribution- and Green’s-function approach to quantum corrections and implications for the melting temperature of two-dimensional Wigner crystals

Quantum corrections to the behavior of a nearly classical system may be determined via the Green's-function formalism, or via the Wigner-distribution-function (WDF) method. Recently, it appeared that there is a serious discrepancy between the results obtained by these methods for the melting temperature of the two-dimensional Wigner crystal. We resolve this problem by showing that the ``effective-potential'' technique of implementing the WDF method is invalid, and we present a correct approach.