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Quantum Measurement and Extended feynman path integral

Communications in Theoretical Physics 2012年第6期57卷 967-982页

作者：文伟白彦魁 Institute of Semiconductors Chinese Academy of Sciences College of Physical Science and Information Engineering Hebei Normal University

Quantum measurement problem has existed many years and inspired a large of literature in both physics and philosophy,but there is still no conclusion and consensus on *** show it can be subsumed into the quantum theory if we extend the feynman path integral by considering the relativistic effect of feynman *** to this extended theory,we deduce not only the Klein-Gordon equation,but also the wave-function-collapse *** is shown that the stochastic and instantaneous collapse of the quantum measurement is due to the "potential noise" of the apparatus or environment and "inner correlation" of wave function ***,the definite-status of the macroscopic matter is due to itself and this does not disobey the quantum *** work will give a new recognition for the measurement problem.

关键词： quantum measurement feynman path integral nonlocal correlation Klein-Gordon equation wave- function- collapse equation

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feynman path integral Using Operator Integration in Banach Space

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Journal of Applied Mathematics and Physics 2024年第2期12卷 432-444页

作者： Reza R. Ahangar Erbil Cetin Serife Muge Ege Mathematics Department Texas A&M University Kingsville USA Mathematics Department Ege University Bornova Türkiye

feynman-path integral in Banach Space: In 1940, R.P. feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits with several walls in terms of Lagrangian instead of Hamiltonian resulted in a magnificent work. It was known as feynman path integrals in quantum physics, and a large part of the scientific community still considers them a heuristic tool that lacks a sound mathematical definition. This paper aims to refute this prejudice, by providing an extensive and self-contained description of the mathematical theory of feynman path Integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. About a hundred years after the beginning of modern physics, it was realized that light could in fact show behavioral characteristics of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same dual behavior, which was later extended to atoms and molecules. We shall follow the method of integration with some modifications to construct a generalized Lebesgue-Bochner-Stieltjes (LBS) integral of the form , where u is a bilinear operator acting in the product of Banach spaces, f is a Bochner summable function, and μ is a vector-valued measure. We will demonstrate that the feynman path integral is consistent and can be justified mathematically with LBS integration approach.

关键词： feynman path integral Lebesgue-Bochner-Stieltjes integral Operator integral Particle-Wave Function Operator Integration Position and Momentum Operators

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