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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 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.

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.

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:

Publisher: Allied Publishers

Published: 2002

Total Pages: 364

ISBN-13: 9788177642315

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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 and Quantum Anomalies

Author: Kazuo Fujikawa

Publisher: Oxford University Press

Published: 2004-04-29

Total Pages: 297

ISBN-13: 0198529139

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The Feynman path integrals are becoming increasingly important in the applications of quantum mechanics and field theory. The path integral formulation of quantum anomalies, i.e. the quantum breaking of certain symmetries, can now cover all the known quantum anomalies in a coherent manner. In this book the authors provide an introduction to the path integral method in quantum field theory and its applications to the analyses of quantum anomalies. No previous knowledge of fieldtheory beyond the advanced undergraduate quantum mechanics is assumed. The book provides the first coherent introductory treatment of the path integral formulation of chiral and Weyl anomalies, with applications to gauge theory in two and four dimensions, conformal field theory and string theory. Explicitand elementary path integral calculations of most of the quantum anomalies covered are given. The conceptual basis of the path integral bosonization in two-dimensional theory, which may have applications to condensed matter theory, for example, is clarified. The book also covers the recent interesting developments in the treatment of fermions and chiral anomalies in lattice gauge theory.

Coherent Evolution in Noisy Environments

Author: Andreas Buchleitner

Publisher: Springer

Published: 2008-01-11

Total Pages: 304

ISBN-13: 3540458557

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In the last two decades extraordinary progress in the experimental handling of single quantum objects has spurred theoretical research into investigating the coupling between quantum systems and their environment. Decoherence, the gradual deterioration of entanglement due to dissipation and noise fed to the system by the environment, has emerged as a central concept. The present set of lectures is intended as a high-level, but self-contained, introduction into the fields of quantum noise and dissipation.In particular their influence on decoherence and applications pertaining to quantum information and quantum communication are studied, leading the nonspecialist researchers and the advanced students gradually to the forefront of research.