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Focusing on the convergence of Feynman's path integral, the book rigorously demonstrates that it aligns with the fundamental solution of the Schrödinger equation under certain conditions related to the potential's differentiability. It details the time slicing method, constructing finite-dimensional integrals that, despite being oscillatory and not absolutely convergent, yield finite values through advanced oscillatory integral techniques. The text is structured in two parts, with the first providing a thorough step-by-step exploration of the time slicing method and the second covering necessary mathematical techniques from functional analysis.
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Rigorous Time Slicing Approach to Feynman Path Integrals, Daisuke Fujiwara
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- Pubblicato
- 2018
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