Semiclassical physics and quantum fluctuations

We investigate theories in which classical and quantum-mechanical degrees of freedom interact dynamically. In commonly used semiclassical theories, such as those used to study inflationary-universe models, quantum fluctuations do not affect the dynamics of the classical variables. We construct a new semiclassical theory in which the quantum and classical fluctuations do affect each other; the Wigner probability function turns out to be a special case. Relevance to calculations of perturbations from inflation are discussed.