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Feynman proposed a postulate or a method of quantization in his celebratedpaper in 1948. Applying Feynman's postulate to temporally continuous quantummeasurements of the positions of particles, Mensky proposed the restrictedFeynman path integrals for continuous quantum measurements afterphenomenological considerations. Our aim in the present paper is to give arigorous proof that Mensky's restricted Feynman path integrals emerge out ofthe Feynman's postulate under a simple approximation. In addition, it is provedthat the restricted Feynman path integrals emerge out of von Neumann'spostulate on instantaneous measurements as well as Feynman's postulate. Thequantum systems that we study include spin systems. These results are appliedto formulations of the multi-split experiments, the quantum Zeno and theAharanov-Bohm effects.

From each of Feynman's and von Neumann's postulates to the restricted  Feynman path integrals: a mathematical theory of temporally continuous  quantum measurements