2020/06/04 by Wataru Ichinose, Ichinose, Wataru
Computer Science · Mathematics · Physics and Astronomy · #46T12 #81P15 #81Q05 #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Information and Cryptography #Quantum Mechanics and Applications #advanced mathematical theories
paper · doi:10.48550/arxiv.2006.02710
openalex publication_date 2020/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The restricted Feynman path integrals (RFPIs) have been proposed to study continuous quantum measurements in physics. The RFPIs are heuristically determined in terms of the usual probability amplitude multiplied by weight for each path, which contains information about the results and the resolution of the measuring device. In the present paper we will consider the RFPIs particularly for the position measurements and will prove rigorously that these RFPIs are well defined in the L2 space and are the solutions to the non-self-adjoint Schroedinger equations. Our results in the present paper give a generalization of the results on the usual Feynman path integrals for the Schroedinger equations.Furthermore, our results are extended to quantum spin systems.