Description of the electrodynamics of a gas by molecular-electromagnetic correlation functions

Starting from basic principles, we develop a description of the electromagnetic interactions of a molecular gas in terms of a set of correlation functions which we call the molecular-electromagnetic correlation functions (MECF's). First we use the energy eigenfunctions for an isolated molecule of the species of interest to define a set of molecular creation and annihilation operators. We then derive a closed set of operator equations for these molecular creation and annihilation operators and the electromagnetic vector potential. Explicit definitions of the lowest-order MECF's are given in terms of these operators, and it is shown how the operator equations which have been obtained can be used to derive equations of motion for the MECF's. Finally, we illustrate the use of the MECF's in describing physical properties of the molecular gas and the electromagnetic field. Brief indications are given of the application of the MECF formulation to the semiclassical approximation and to the description of quantum emission of radiation, topics which are treated in greater detail in subsequent papers. The basic MECF formulation described here contains three rather mild approximations: (1) Atomic nuclei are treated as elementary particles; (2) nuclei and electrons are treated nonrelativistically; and (3) the effect of molecular collisions with the container walls on the internal molecular state is neglected. Consequently, the physical description contained in the formulation is rather complete; and the MECF results can be used both to provide a sound basis for some aspects of the usual heuristic models, and to ascertain the ways in which those models are incomplete