Rigorous Time Slicing Approach to Feynman Path Integrals

• Main Author: Fujiwara, Daisuke (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Tokyo : Springer Japan : Imprint: Springer, 2017.
• Series: Mathematical Physics Studies,
• Subjects: Mathematics.; Fourier analysis.; Functional analysis.; Partial differential equations.; Mathematical physics.; Mathematical Physics.; Functional Analysis.; Partial Differential Equations.; Fourier Analysis.

This book proves that Feynman's original definition of the path integral actually converges to the fundamental solution of the Schrödinger equation at least in the short term if the potential is differentiable sufficiently many times and its derivatives of order equal to or higher than two are...

Table of Contents:

• Part I Convergence of Time Slicing Approximation of Feynman Path Integrals
• 1 Feynman’s idea
• 2 Assumption on Potentials
• 3 Path Integrals and Oscillatory Integrals
• 4 Statement of Main Results
• 5 Convergence of Feynman Path Integrals
• 6 Feynman Path Integral and Schr¨odinger Equation
• Part II Supplement–Some Results of Real Analysis
• 7 Kumano-go–Taniguchi Theorem
• 8 Stationary Phase Method for Oscillatory Integrals over a Space of Large Dimension
• 9 L2-boundedness of Oscillatory Integral Operators
• Bibliography
• Index.