Mathematical Feynman Path Integrals And Their Applications Second Edition
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Mathematical Feynman Path Integrals And Their Applications
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Author : Sonia Mazzucchi
language : en
Publisher: World Scientific
Release Date : 2009
Mathematical Feynman Path Integrals And Their Applications written by Sonia Mazzucchi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Although more than 60 years have passed since their first appearance, Feynman path integrals have yet to lose their fascination and luster. They are not only a formidable instrument of theoretical physics, but also a mathematical challenge; in fact, several mathematicians in the last 40 years have devoted their efforts to the rigorous mathematical definition of Feynman''s ideas. This volume provides a detailed, self-contained description of the mathematical difficulties as well as the possible techniques used to solve these difficulties. In particular, it gives a complete overview of the mathematical realization of Feynman path integrals in terms of well-defined functional integrals, that is, the infinite dimensional oscillatory integrals. It contains the traditional results on the topic as well as the more recent developments obtained by the author. Mathematical Feynman Path Integrals and Their Applications is devoted to both mathematicians and physicists, graduate students and researchers who are interested in the problem of mathematical foundations of Feynman path integrals.
Mathematical Feynman Path Integrals And Their Applications Second Edition
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Author : Sonia Mazzucchi
language : en
Publisher: World Scientific
Release Date : 2021-11-16
Mathematical Feynman Path Integrals And Their Applications Second Edition written by Sonia Mazzucchi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-16 with Science categories.
Feynman path integrals are ubiquitous in quantum physics, even if a large part of the scientific community still considers them as a heuristic tool that lacks a sound mathematical definition. Our book aims to refute this prejudice, 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.This second edition presents a detailed discussion of the general theory of complex integration on infinite dimensional spaces, providing on one hand a unified view of the various existing approaches to the mathematical construction of Feynman path integrals and on the other hand a connection with the classical theory of stochastic processes. Moreover, new chapters containing recent applications to several dynamical systems have been added.This book bridges between the realms of stochastic analysis and the theory of Feynman path integration. It is accessible to both mathematicians and physicists.
Mathematical Theory Of Feynman Path Integrals
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Author : Sergio Albeverio
language : en
Publisher: Springer
Release Date : 2008-05-06
Mathematical Theory Of Feynman Path Integrals written by Sergio Albeverio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-06 with Mathematics categories.
The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.
Introduction To Random Time And Quantum Randomness New Edition
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Author : Kai Lai Chung
language : en
Publisher: World Scientific
Release Date : 2003-05-28
Introduction To Random Time And Quantum Randomness New Edition written by Kai Lai Chung and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-28 with Mathematics categories.
This book is made up of two essays on the role of time in probability and quantum physics. In the first one, K L Chung explains why, in his view, probability theory starts where random time appears. This idea is illustrated in various probability schemes and the deep impact of those random times on the theory of the stochastic process is shown.In the second essay J-C Zambrini shows why quantum physics is not a regular probabilistic theory, but also why stochastic analysis provides new tools for analyzing further the meaning of Feynman's path integral approach and a number of foundational issues of quantum physics far beyond what is generally considered. The role of the time parameter, in this theory, is critically re-examined and a fresh way to approach the long-standing problem of the quantum time observable is suggested.
Quantum Mechanics
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Author : Gregory L. Naber
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-09-20
Quantum Mechanics written by Gregory L. Naber and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-20 with Science categories.
This work covers quantum mechanics by answering questions such as where did the Planck constant and Heisenberg algebra come from, what motivated Feynman to introduce his path integral and why does one distinguish two types of particles, the bosons and fermions. The author addresses all these topics with utter mathematical rigor. The high number of instructive Appendices and numerous Remark sections supply the necessary background knowledge.
When Form Becomes Substance
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Author : Luciano Boi
language : en
Publisher: Springer Nature
Release Date : 2022-11-30
When Form Becomes Substance written by Luciano Boi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-30 with Science categories.
This interdisciplinary volume collects contributions from experts in their respective fields with as common theme diagrams. Diagrams play a fundamental role in the mathematical visualization and philosophical analysis of forms in space. Some of the most interesting and profound recent developments in contemporary sciences, whether in topology, geometry, dynamic systems theory, quantum field theory or string theory, have been made possible by the introduction of new types of diagrams, which, in addition to their essential role in the discovery of new classes of spaces and phenomena, have contributed to enriching and clarifying the meaning of the operations, structures and properties that are at the heart of these spaces and phenomena. The volume gives a closer look at the scope and the nature of diagrams as constituents of mathematical and physical thought, their function in contemporary artistic work, and appraise, in particular, the actual importance of the diagrams of knots, of braids, of fields, of interaction, of strings in topology and geometry, in quantum physics and in cosmology, but also in theory of perception, in plastic arts and in philosophy. The editors carefully curated this volume to be an inspiration to students and researchers in philosophy, phenomenology, mathematics and the sciences, as well as artists, musicians and the general interested audience.
Seminar On Stochastic Analysis Random Fields And Applications Vi
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Author : Robert Dalang
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-16
Seminar On Stochastic Analysis Random Fields And Applications Vi written by Robert Dalang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-16 with Mathematics categories.
This volume contains refereed research or review papers presented at the 6th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, in May 2008. The seminar focused mainly on stochastic partial differential equations, especially large deviations and control problems, on infinite dimensional analysis, particle systems and financial engineering, especially energy markets and climate models. The book will be a valuable resource for researchers in stochastic analysis and professionals interested in stochastic methods in finance.
Stochastic Analysis And Mathematical Physics Anestoc 96 Proceedings Of The 2nd International Workshop
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Author : Rolando Rebolledo
language : en
Publisher: World Scientific
Release Date : 1998-09-02
Stochastic Analysis And Mathematical Physics Anestoc 96 Proceedings Of The 2nd International Workshop written by Rolando Rebolledo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-02 with categories.
A Modern Approach To Functional Integration
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Author : John R. Klauder
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-08
A Modern Approach To Functional Integration written by John R. Klauder and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-08 with Mathematics categories.
This text takes advantage of recent developments in the theory of path integration and attempts to make a major paradigm shift in how the art of functional integration is practiced. The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and applied mathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. A Modern Approach to Functional Integration offers insight into a number of contemporary research topics, which may lead to improved methods and results that cannot be found elsewhere in the textbook literature. Exercises are included in most chapters, making the book suitable for a one-semester graduate course on functional integration.
Wave Packet Analysis Of Feynman Path Integrals
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Author : Fabio Nicola
language : en
Publisher: Springer Nature
Release Date : 2022-07-28
Wave Packet Analysis Of Feynman Path Integrals written by Fabio Nicola and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-28 with Science categories.
The purpose of this monograph is to offer an accessible and essentially self-contained presentation of some mathematical aspects of the Feynman path integral in non-relativistic quantum mechanics. In spite of the primary role in the advancement of modern theoretical physics and the wide range of applications, path integrals are still a source of challenging problem for mathematicians. From this viewpoint, path integrals can be roughly described in terms of approximation formulas for an operator (usually the propagator of a Schrödinger-type evolution equation) involving a suitably designed sequence of operators. In keeping with the spirit of harmonic analysis, the guiding theme of the book is to illustrate how the powerful techniques of time-frequency analysis - based on the decomposition of functions and operators in terms of the so-called Gabor wave packets – can be successfully applied to mathematical path integrals, leading to remarkable results and paving the way to a fruitful interaction. This monograph intends to build a bridge between the communities of people working in time-frequency analysis and mathematical/theoretical physics, and to provide an exposition of the present novel approach along with its basic toolkit. Having in mind a researcher or a Ph.D. student as reader, we collected in Part I the necessary background, in the most suitable form for our purposes, following a smooth pedagogical pattern. Then Part II covers the analysis of path integrals, reflecting the topics addressed in the research activity of the authors in the last years.