  Quantum Field Theory (QFT) makes predictions by combining two sets of
assumptions: (1) quantum dynamics, such as a Schrodinger or Liouville equation;
(2) quantum measurement, such as stochastic collapse to an eigenfunction of a
measurement operator. A previous paper defined a classical density matrix R
encoding the statistical moments of an ensemble of states of classical
second-order Hamiltonian field theory. It proved Tr(RQ)=E(Q), etc., for the
usual field operators as defined by Weinberg, and it proved that those
observables of the classical system obey the usual Heisenberg dynamic equation.
However, R itself obeys dynamics different from the usual Liouville equation!
This paper derives those dynamics and the discrepancy between CFT and normal
form QFT in predicting any observables g(Q,P). There is some preliminary
evidence for the conjecture that the discrepancies disappear in equilibrium
states (bound states and scattering states) for finite bosonic field theories.
Even if not, they appear small enough to warrant reconsideration of CFT as a
theory of dynamics. Appendix proposes alternative closure of turbulence based
on modified Bogliubov transforms, an application where ordinary ones become
undefined.
