Quantum state diffusion, measurement and second quantization

Realistic dynamical theories of measurement based on the diffusion of quantum states are nonunitary, whereas quantum field theory and its generalizations are unitary. This problem in the quantum field theory of quantum state diffusion (QSD) appears already in the Lagrangian formulation of QSD as a classical equation of motion, where Liouville's theorem does not apply to the usual field theory formulation. This problem is resolved here by doubling the number of freedoms used to represent a quantum field. The space of quantum fields is then a classical configuration space, for which volume need not be conserved, instead of the usual phase space, to which Liouville's theorem applies. The creation operator for the quantized field satisfies the QSD equations, but the annihilation operator does not satisfy the conjugate eqation. It appears only in a formal role.