  To apply the abstract quantum formalism to a particular physical system, one
must specify the precise form of the relevant measurement and symmetry
transformation operators. These operators are determined by a set of rules, the
correspondence rules of quantum theory. The physical origin of these rules is
obscure, and their physical interpretation and their degree of generality is
presently unclear. In this paper, we show that all of the commonly-used
correspondence rules can be systematically derived from a new physical
principle, the Average-Value Correspondence Principle. This principle shows
that the correspondence rules result from the systematic translation of
relations between measurement results known to hold in a classical model of a
system, providing these rules with a clear physical interpretation, and clearly
demarcating their domain of applicability.
