  We formulate a novel approach to decoherence based on neglecting
observationally inaccessible correlators. We apply our formalism to a
renormalised interacting quantum field theoretical model. Using
out-of-equilibrium field theory techniques we show that the Gaussian von
Neumann entropy for a pure quantum state increases to the interacting thermal
entropy. This quantifies decoherence and thus measures how classical our pure
state has become. The decoherence rate is equal to the single particle decay
rate in our model. We also compare our approach to existing approaches to
decoherence in a simple quantum mechanical model. We show that the entropy
following from the perturbative master equation suffers from physically
unacceptable secular growth.
