Decoherence of Correlation Histories

We use a $\lambda\Phi^4$ scalar quantum field theory to illustrate a new approach to the study of quantum to classical transition. In this approach, the decoherence functional is employed to assign probabilities to consistent histories defined in terms of correlations among the fields at separate points, rather than the field itself. We present expressions for the quantum amplitudes associated with such histories, as well as for the decoherence functional between two of them. The dynamics of an individual consistent history may be described by a Langevin-type equation, which we derive. \noindent {\it Dedicated to Professor Brill on the occasion of his sixtieth birthday, August 1993}