In this book the mathematical foundations of quantum theory are developed
in a way which is well adapted to the analysis of open quantum mechanical
systems. The relatively recent development of non-equilibrium quantum
statistical mechanics as a rigorous mathematical discipline, and continuing
research into measurement theory, have led to the realisation that there is
considerable advantage in laying the foundations of the subject in a more
general and flexible manner than was done by von Neumann in the early
days of the subject.
Undoubtedly the new approach owes a great deal to the extraordinary
fertility of the field of quantum optics. The experimental investigation of the
statistics of coherent photon beams by the measurement of multiparticle
correlation functions fits very unnaturally into the framework of ortho-
complemented lattices and projection-valued measures. Indeed the
measurement of waiting times for the arrival of photons at counters runs completely
counter to the philosophy that "ideal" measurements can be considered as
taking place at an instant of time.