Wave Packet Analysis Of Feynman Path Integrals

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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.

Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets

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Author : Hagen Kleinert
language : en
Publisher: World Scientific
Release Date : 2009

Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets written by Hagen Kleinert 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 Business & Economics categories.

Topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern-Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect." "The relevance of path integrals to financial markets is discussed, and improvements of the famous Black-Scholes formula for option prices are developed which account for the fact that large market fluctuations occur much more frequently than in Gaussian distributions." --Book Jacket.

Techniques And Applications Of Path Integration

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Author : L. S. Schulman
language : en
Publisher: Courier Corporation
Release Date : 2012-10-10

Techniques And Applications Of Path Integration written by L. S. Schulman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-10 with Science categories.

Suitable for advanced undergraduates and graduate students, this text develops the techniques of path integration and deals with applications, covering a host of illustrative examples. 26 figures. 1981 edition.

Path Integral Methods And Their Applications

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Author : K V Bhagwat
language : en
Publisher: World Scientific
Release Date : 1993-04-28

Path Integral Methods And Their Applications written by K V Bhagwat and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-04-28 with Science categories.

This book presents the major developments in this field with emphasis on application of path integration methods in diverse areas. After introducing the concept of path integrals, related topics like random walk, Brownian motion and Wiener integrals are discussed. Several techniques of path integration including global and local time transformations, numerical methods as well as approximation schemes are presented. The book provides a proper perspective of some of the most recent exact results and approximation schemes for practical applications.

Handbook Of Feynman Path Integrals

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Author : Christian Grosche
language : en
Publisher: Springer
Release Date : 2013-11-13

Handbook Of Feynman Path Integrals written by Christian Grosche and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-13 with Science categories.

The Handbook of Feynman Path Integrals appears just fifty years after Richard Feynman published his pioneering paper in 1948 entitled "Space-Time Approach to Non-Relativistic Quantum Mechanics", in which he introduced his new formulation of quantum mechanics in terms of path integrals. The book presents for the first time a comprehensive table of Feynman path integrals together with an extensive list of references; it will serve the reader as a thorough introduction to the theory of path integrals. As a reference book, it is unique in its scope and will be essential for many physicists, chemists and mathematicians working in different areas of research.

Feynman S Thesis

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Author : Richard Phillips Feynman
language : en
Publisher: World Scientific
Release Date : 2005

Feynman S Thesis written by Richard Phillips Feynman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.

Richard Feynman's never previously published doctoral thesis formed the heart of much of his brilliant and profound work in theoretical physics. Entitled ?The Principle of Least Action in Quantum Mechanics," its original motive was to quantize the classical action-at-a-distance electrodynamics. Because that theory adopted an overall space?time viewpoint, the classical Hamiltonian approach used in the conventional formulations of quantum theory could not be used, so Feynman turned to the Lagrangian function and the principle of least action as his points of departure.The result was the path integral approach, which satisfied ? and transcended ? its original motivation, and has enjoyed great success in renormalized quantum field theory, including the derivation of the ubiquitous Feynman diagrams for elementary particles. Path integrals have many other applications, including atomic, molecular, and nuclear scattering, statistical mechanics, quantum liquids and solids, Brownian motion, and noise theory. It also sheds new light on fundamental issues like the interpretation of quantum theory because of its new overall space?time viewpoint.The present volume includes Feynman's Princeton thesis, the related review article ?Space?Time Approach to Non-Relativistic Quantum Mechanics? [Reviews of Modern Physics 20 (1948), 367?387], Paul Dirac's seminal paper ?The Lagrangian in Quantum Mechanics'' [Physikalische Zeitschrift der Sowjetunion, Band 3, Heft 1 (1933)], and an introduction by Laurie M Brown.

An Introduction To Quantum Theory

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Author : Jeff Greensite
language : en
Publisher:
Release Date : 2017

An Introduction To Quantum Theory written by Jeff Greensite and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Quantum theory categories.

"Written in a lucid and engaging style, the author takes readers from an overview of classical mechanics and the historical development of quantum theory through to advanced topics. The mathematical aspects of quantum theory necessary for a firm grasp of the subject are developed in the early chapters, but an effort is made to motivate that formalism on physical grounds. Including animated figures and their respective Mathematica{reg} codes, this book provides a complete and comprehensive text for students in physics, maths, chemistry and engineering needing an accessible introduction to quantum mechanics."--Prové de l'editor.

Path Integrals And Anomalies In Curved Space

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Author : Fiorenzo Bastianelli
language : en
Publisher: Cambridge University Press
Release Date : 2006-07-20

Path Integrals And Anomalies In Curved Space written by Fiorenzo Bastianelli and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-20 with Science categories.

This book introduces path integrals, a powerful method for describing quantum phenomena, and then uses them to compute anomalies in quantum field theories. An advanced text for researchers and graduate students of quantum field theory and string theory, it also provides a stand-alone introduction to path integrals in quantum mechanics.

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 Science 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.

Path Integrals And Quantum Processes

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Author : Mark S. Swanson
language : en
Publisher: Academic Press
Release Date : 2012-12-02

Path Integrals And Quantum Processes written by Mark S. Swanson and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Science categories.

In a clearly written and systematic presentation, Path Integrals and Quantum Processes covers all concepts necessary to understand the path integral approach to calculating transition elements, partition functions, and source functionals. The book, which assumes only a familiarity with quantum mechanics, is ideal for use as a supplemental textbook in quantum mechanics and quantum field theory courses. Graduate and post-graduate students who are unfamiliar with the path integral will also benefit from this contemporary text. Exercise sets are interspersed throughout the text to facilitate self-study. - Explicates the relationship between the operator and path integral formulations of quantum mechanics and quantum field theory - Provides a systematic and detailed presentation of Grassmann variables - Covers Dirac's method of constraints and the relationship of ghosts, gauge invariance, and gauge conditions in gauge field theory - Includes applications to statistical mechanics, the effective action and potential, and anomaly analysis