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- W3033077804 abstract "It has been stated in the physics literature that the probability amplitude for a quantum system after a continuous position measurement can be expressed by the restricted or the weighted Feynman path integral containing information about the result and the resolution of its measurement. In the present paper it is proved that the restricted Feynman path integrals can be defined in a rigorous sense. More specifically, we consider a quantum system consisting of some particles and simultaneously perform a continuous measurement of the positions of all particles in the time interval $[0,T]$. Then, it is shown rigorously that the restricted Feynman path integral after the measurement can be defined in the $L^2$ space and satisfies the corresponding non-self-adjoint Schroeodinger equation. In addition, our results are generalized to a quantum spin system where a continuous position measurement for all spin components of all particles is simultaneously performed, though the results obtained are inadequate for general use." @default.
- W3033077804 created "2020-06-12" @default.
- W3033077804 creator A5062551877 @default.
- W3033077804 date "2020-06-04" @default.
- W3033077804 modified "2023-09-27" @default.
- W3033077804 title "A mathematical theory of the Feynman path integrals for continuous quantum position measurements" @default.
- W3033077804 hasPublicationYear "2020" @default.
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