ON THEORY OF THE STATISTICAL GENERATING FUNCTIONAL FOR THE ORDER PARAMETER (II) —DENSITY MATRIX AND THE FIELD-THEORETICAL STRUCTURE OF THE GENERATING FUNCTIONAL

Several equivalent expressions for the generating functional of the order parameter are derived in this paper to elucidate how the statistical properties are incorporated in its field-theoretical structure. It is shown that in the process of determining the generating the dynamic evolution and the statistical information can be seperated to a certain extent which facilitates solving the problem. The whole procedure is greatly simplified if the statistical correlation is Gaussian or a generalized fluctuation-dissipaticn theorem (FDT) holds. As an example, the Gaussian character of the thermal equilibrium distribution is justified and the Matsubara technique along the imaginary time axis is extended to the real axis to provide a complete perturbation scheme for the closed time-path Green's functions (CTPGF).