Coupling ``Classical'' and Quantum Variables

Experimentally, certain degrees of freedom may appear classical because their quantum fluctuations are smaller than the experimental error associated with measuring them. An approximation to a fully quantum theory is described in which the self-interference of such ``quasiclassical'' variables is neglected so that they behave classically when not coupled to other quantum variables. Coupling to quantum variables can lead to evolution in which quasiclassical variables do not have definite values, but values which are correlated to the state of the quantum variables. A mathematical description implementing this backreaction of the quantum variables on the quasiclassical variables is critically discussed.