CONTINUOUS QUANTUM MEASUREMENT - LOCAL AND GLOBAL APPROACHES

In 1979 B. Menski suggested a formula for the linear propagator of a q uantum system with continuously observed position in terms of a heuris tic Feynman path integral. In 1989 the aposterior linear stochastic Sc hrojdinger equation was derived by V. P. Belavkin describing the evolu tion of a quantum system under continuous (nondemolition) measurement. In the present paper, these two approaches to the description of cont inuous quantum measurement are brought together from the point of view of physics as well as mathematics. A self-contained deductions of bot h Menski's formula and the Belavkin equation is given, and the new ins ights in the problem provided by the local (stochastic equation) appro ach to the problem are described. Furthermore, a mathematically well-d efined representations of the solution of the aposterior Schrodinger e quation in terms of the path integral is constructed and shown to be h euristically equivalent to the Menski propagator.