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Mathematical Feynman Path Integrals And Their Applications (Second Edition)

Author: Sonia Mazzucchi

Publisher: World Scientific

Published: 2021-11-16

Total Pages: 360

ISBN-13: 9811214808

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

Author: Sergio Albeverio

Publisher: Springer

Published: 2008-05-06

Total Pages: 184

ISBN-13: 3540769560

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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.

Mathematical Theory of Feynman Path Integrals

Author: Sergio A. Albeverio

Publisher: Springer

Published: 2006-11-14

Total Pages: 143

ISBN-13: 354038250X

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Feynman path integrals integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low dimensional topology and differential geometry, algebraic geometry, infinite dimensional analysis and geometry, and number theory. 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. To take care of the many developments which have occurred since then, an entire new chapter about the current forefront of research has been added. Except for this new chapter, the basic material and presentation of the first edition was mantained, a few misprints have been corrected. At the end of each chapter the reader will also find notes with further bibliographical information.

Techniques and Applications of Path Integration

Author: L. S. Schulman

Publisher: Courier Corporation

Published: 2012-10-10

Total Pages: 434

ISBN-13: 0486137023

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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.

Functional Integration and Quantum Physics

Author: Barry Simon

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 322

ISBN-13: 0821835823

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Focuses on probabilistic foundations of the Feynman-Kac formula. Starting with main examples of Gaussian processes (the Brownian motion, the oscillatory process, and the Brownian bridge), this book presents four different proofs of the Feynman-Kac formula.

Quantum Mechanics and Path Integrals [by] R.P. Feynman [and] A.R. Hibbs

Author: Richard Phillips Feynman

Publisher:

Published: 1965

Total Pages: 0

ISBN-13: 9780071139489

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Path-integral Methods and Their Applications

Author: D. C. Khandekar

Publisher: World Scientific

Published: 1993

Total Pages: 362

ISBN-13: 9789810205638

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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.

Path Integrals and Quantum Processes

Author: Mark S. Swanson

Publisher: Courier Corporation

Published: 2014-02-19

Total Pages: 464

ISBN-13: 0486782301

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Graduate-level, systematic presentation of path integral approach to calculating transition elements, partition functions, and source functionals. Covers Grassmann variables, field and gauge field theory, perturbation theory, and nonperturbative results. 1992 edition.

Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets

Author: Hagen Kleinert

Publisher: World Scientific

Published: 2009

Total Pages: 1626

ISBN-13: 9814273570

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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.

Path Integrals in Physics

Author: M Chaichian

Publisher: CRC Press

Published: 2001-07-01

Total Pages: 420

ISBN-13: 9780750307130

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Path Integrals in Physics: Volume I, Stochastic Processes and Quantum Mechanics presents the fundamentals of path integrals, both the Wiener and Feynman type, and their many applications in physics. Accessible to a broad community of theoretical physicists, the book deals with systems possessing a infinite number of degrees in freedom. It discusses the general physical background and concepts of the path integral approach used, followed by a detailed presentation of the most typical and important applications as well as problems with either their solutions or hints how to solve them. It describes in detail various applications, including systems with Grassmann variables. Each chapter is self-contained and can be considered as an independent textbook. The book provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers. The path integral approach has proved extremely useful for the understanding of the most complex problems in quantum field theory, cosmology, and condensed matter physics. Path Integrals in Physics: Volume II, Quantum Field Theory, Statistical Physics and other Modern Applications covers the fundamentals of path integrals, both the Wiener and Feynman types, and their many applications in physics. The book deals with systems that have an infinite number of degrees of freedom. It discusses the general physical background and concepts of the path integral approach used, followed by a detailed presentation of the most typical and important applications as well as problems with either their solutions or hints how to solve them. Each chapter is self-contained and can be considered as an independent textbook. It provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers.