FUNCTIONAL METHODS IN STATISTICAL MECHANICS .I. CLASSICAL THEORY

A statistical-mechanical theory of fields is developed. Since a field has an infinite number of degrees of freedom, it is natural and convenient to use functional methods for its description. The most general statistical-mechanical state for a field is represented by a distribution functional which satisfies a functional differential equation analogous to the Liouville equation. The functional Fourier transform (characteristic functional) is introduced and its properties are studied. Multitime functional and various reduced distribution functions are also discussed. The formalism is applied to the free electromagnetic fields as well as to a system of charged particles (plasma) interacting via the electromagnetic field.