Functional Integral Formulations for Classical Fluids

Various functional integral formalisms of classical monatomic fluids are considered with their applicabilities and limitations compared. For length scales large compared to the particle size, the density field theory, in which the action of the functional integral is simply given by the mean fieldfree energy functional expression, is shown to be a well-defined and rigorous formulation. For short range properties of dense fluids, a different version of the functional integral method is developed by explicitly separating out the hard core part of the interaction. The resulting functional integral is seen to require correlation functions of the hard sphere fluid as the input. The generalized van der Waals equation and the random phase approximation of the cluster diagrammatic methods are recovered simply as the stationary-phase approximation and its Gaussian correction to the functional integral, respectively.