Shortcuts
Top of page (Alt+0)
Page content (Alt+9)
Page menu (Alt+8)
Your browser does not support javascript, some WebOpac functionallity will not be available.
.
Default
.
PageMenu
-
Main Menu
-
Simple Search
.
Advanced Search
.
Journal Search
.
Refine Search Results
.
Preferences
.
Search Menu
Simple Search
.
Advanced Search
.
New Items Search
.
Journal Search
.
Refine Search Results
.
Bottom Menu
Help
Italian
.
English
.
German
.
New Item Menu
New Items Search
.
New Items List
.
Links
SISSA Library
.
ICTP library
.
Italian National web catalog (SBN)
.
Trieste University web catalog
.
Udine University web catalog
.
© LIBERO v6.4.1sp220816
Page content
You are here
:
Catalogue Display
Catalogue Display
Rigorous Time Slicing Approach to Feynman Path Integrals
.
Bookmark this Record
Catalogue Record 37951
.
.
Author info on Wikipedia
.
.
LibraryThing
.
.
Google Books
.
.
Amazon Books
.
Catalogue Information
Catalogue Record 37951
.
Reviews
Catalogue Record 37951
.
British Library
Resolver for RSN-37951
Google Scholar
Resolver for RSN-37951
WorldCat
Resolver for RSN-37951
Catalogo Nazionale SBN
Resolver for RSN-37951
GoogleBooks
Resolver for RSN-37951
ICTP Library
Resolver for RSN-37951
.
Share Link
Jump to link
Catalogue Information
Field name
Details
Dewey Class
530.15
Title
Rigorous Time Slicing Approach to Feynman Path Integrals ([EBook]) / by Daisuke Fujiwara.
Author
Fujiwara, Daisuke
Other name(s)
SpringerLink (Online service)
Publication
Tokyo : : Springer Japan : : Imprint: Springer, , 2017.
Physical Details
IX, 333 p. 1 illus. : online resource.
Series
Mathematical physics studies
0921-3767
ISBN
9784431565536
Summary Note
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 bounded. The semi-classical asymptotic formula up to the second term of the fundamental solution is also proved by a method different from that of Birkhoff. A bound of the remainder term is also proved. The Feynman path integral is a method of quantization using the Lagrangian function, whereas Schrödinger's quantization uses the Hamiltonian function. These two methods are believed to be equivalent. But equivalence is not fully proved mathematically, because, compared with Schrödinger's method, there is still much to be done concerning rigorous mathematical treatment of Feynman's method. Feynman himself defined a path integral as the limit of a sequence of integrals over finite-dimensional spaces which is obtained by dividing the time interval into small pieces. This method is called the time slicing approximation method or the time slicing method. This book consists of two parts. Part I is the main part. The time slicing method is performed step by step in detail in Part I. The time interval is divided into small pieces. Corresponding to each division a finite-dimensional integral is constructed following Feynman's famous paper. This finite-dimensional integral is not absolutely convergent. Owing to the assumption of the potential, it is an oscillatory integral. The oscillatory integral techniques developed in the theory of partial differential equations are applied to it. It turns out that the finite-dimensional integral gives a finite definite value. The stationary phase method is applied to it. Basic properties of oscillatory integrals and the stationary phase method are explained in the book in detail. Those finite-dimensional integrals form a sequence of approximation of the Feynman path integral when the division goes finer and finer. A careful discussion is required to prove the convergence of the approximate sequence as the length of each of the small subintervals tends to 0. For that purpose the book uses the stationary phase method of oscillatory integrals over a space of large dimension, of which the detailed proof is given in Part II of the book. By virtue of this method, the approximate sequence converges to the limit. This proves that the Feynman path integral converges. It turns out that the convergence occurs in a very strong topology. The fact that the limit is the fundamental solution of the Schrödinger equation is proved also by the stationary phase method. The semi-classical asymptotic formula naturally follows from the above discussion. A prerequisite for readers of this book is standard knowledge of functional analysis. Mathematical techniques required here are explained and proved from scratch in Part II, which occupies a large part of the book, because they are considerably different from techniques usually used in treating the Schrödinger equation.:
Contents note
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.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-4-431-56553-6
Links to Related Works
Subject References:
Fourier Analysis
.
Functional Analysis
.
Mathematical Physics
.
Mathematics
.
Partial differential equations
.
Authors:
Fujiwara, Daisuke
.
Corporate Authors:
SpringerLink (Online service)
.
Series:
Mathematical physics studies
.
Classification:
530.15
.
.
ISBD Display
Catalogue Record 37951
.
Tag Display
Catalogue Record 37951
.
Related Works
Catalogue Record 37951
.
Marc XML
Catalogue Record 37951
.
Add Title to Basket
Catalogue Record 37951
.
Catalogue Information 37951
Beginning of record
.
Catalogue Information 37951
Top of page
.
Download Title
Catalogue Record 37951
Export
This Record
As
Labelled Format
Bibliographic Format
ISBD Format
MARC Format
MARC Binary Format
MARCXML Format
User-Defined Format:
Title
Author
Series
Publication Details
Subject
To
File
Email
Reviews
This item has not been rated.
Add a Review and/or Rating
37951
1
37951
-
2
37951
-
3
37951
-
4
37951
-
5
37951
-
Quick Search
Search for