PRINCIPLE OF STATIONARY ACTION AND THE DEFINITION OF A PROPER OPEN SYSTEM

The generalization of the variation of the action-integral operator in troduced by Schwinger in the derivation of the principle of stationary action enables one to use this principle to obtain a description of t he quantum mechanics of an open system. It is shown that augmenting th e Lagrange-function operator by the divergence of the gradient of the density operator, a process which leaves the equations of motion unalt ered, leads to a class of generators whose associated infinitesimal tr ansformations yield variations of the action-integral operator for an open system, similar in form and content to those obtained for the tot al, isolated system. The augmented Lagrange-function operator and the associated action-integral operator are termed proper operators, since only their variation yields equations of motion for the observables o f an open system, in agreement with the expressions obtained from the field equations. Modifying the generator in this manner is shown to be equivalent to requiring that the open system be bounded by a surface through which there is a local zero flux in the gradient vector field of the electron density. Only the observables of such properly defined open systems are described by the correct equations of motion. The ph ysical significance of such proper open systems is discussed.