Path Integrals In Quantum Mechanics Statistics And Polymer Physics

Author : Hagen Kleinert
Publisher : World Scientific
Page : 1626 pages
File Size : 54,6 Mb
Release : 2009
Category : Business & Economics
ISBN : 9789814273572

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Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets by Hagen Kleinert Pdf

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.

Author : Hagen Kleinert
Publisher : World Scientific Publishing Company Incorporated
Page : 664 pages
File Size : 44,8 Mb
Release : 1990-01-01
Category : Science
ISBN : 9810201974

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Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics by Hagen Kleinert Pdf

Author : Hagen Kleinert
Publisher : World Scientific Publishing Company
Page : 1505 pages
File Size : 54,8 Mb
Release : 2004-03-05
Category : Electronic
ISBN : 9789813106024

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Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets by Hagen Kleinert Pdf

This is the third, significantly expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have become possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r2 potentials. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations. In addition to the time-sliced definition, the author gives a perturbative definition of path integrals which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely integrals over products of distributions. The powerful Feynman–Kleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent expansions. The convergence is uniform from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals. Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions. A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory also applies now to small orders. Special attention is devoted to path integrals with 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 given which account for the fact that large market fluctuations occur much more frequently than in the commonly used Gaussian distributions. The author's other book on 'Critical Properties of Φ4 Theories' gives a thorough introduction to the field of critical phenomena and develops new powerful resummation techniques for the extraction of physical results from the divergent perturbation expansions. Request Inspection Copy

Author : Hagen Kleinert
Publisher : World Scientific Publishing Company Incorporated
Page : 891 pages
File Size : 49,6 Mb
Release : 1995
Category : Science
ISBN : 9810214723

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Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics by Hagen Kleinert Pdf

Author : Hagen Kleinert
Publisher : Unknown
Page : 1593 pages
File Size : 49,5 Mb
Release : 2006
Category : Electronic
ISBN : 9812772855

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Path Integrals In Quantum Mechanics, Statistics, Polymer Physics, And Financial Markets (4th Edition). by Hagen Kleinert Pdf

Author : R. J. Rivers
Publisher : Cambridge University Press
Page : 356 pages
File Size : 41,8 Mb
Release : 1988-10-27
Category : Science
ISBN : 0521368707

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Path Integral Methods in Quantum Field Theory by R. J. Rivers Pdf

The applications of functional integral methods introduced in this text for solving a range of problems in quantum field theory will prove useful for students and researchers in theoretical physics and quantum field theory.

Author : Asim O. Barut,Wesley E. Brittin
Publisher : Unknown
Page : 458 pages
File Size : 44,5 Mb
Release : 1971
Category : Science
ISBN : UOM:39015017803308

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Lectures in Theoretical Physics by Asim O. Barut,Wesley E. Brittin Pdf

Author : Hagen Kleinert
Publisher : World Scientific
Page : 1512 pages
File Size : 49,8 Mb
Release : 2004
Category : Science
ISBN : 9812381074

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Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets by Hagen Kleinert Pdf

This is the third, significantly expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have become possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r2 potentials. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations. In addition to the time-sliced definition, the author gives a perturbative definition of path integrals which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely integrals over products of distributions. The powerful Feynman -- Kleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent expansions. The convergence is uniform from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals. Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbationexpansions. A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory also applies now to small orders. Special attention is devoted to path integrals with 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 Chem-Simons theory of particles with fractional statistics (anyohs) 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 given which account for the fact that large market fluctuations occur much more frequently than in the commonly used Gaussian distributions.

Author : Frederik W. Wiegel
Publisher : World Scientific
Page : 226 pages
File Size : 51,5 Mb
Release : 1986
Category : Science
ISBN : 9971978709

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Introduction to Path-integral Methods in Physics and Polymer Science by Frederik W. Wiegel Pdf

This monograph distills material prepared by the author for class lectures, conferences and research seminars. It fills in a much-felt gap between the older and original work by Feynman and Hibbs and the more recent and advanced volume by Schulman. After presenting an elementary account on the Wiener path integral as applied to Brownian motion, the author progresses on to the statistics of polymers and polymer entanglements. The next three chapters provide an introduction to quantum statistical physics with emphasis on the conceptual understanding of many-variable systems. A chapter on the renormalization group provides material for starting on research work. The final chapter contains an over view of the role of path integrals in recent developments in physics. A good bibliography is provided for each chapter.

Author : Lukong Cornelius Fai
Publisher : CRC Press
Page : 415 pages
File Size : 53,9 Mb
Release : 2021-04-15
Category : Science
ISBN : 9781000349047

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Feynman Path Integrals in Quantum Mechanics and Statistical Physics by Lukong Cornelius Fai Pdf

This book provides an ideal introduction to the use of Feynman path integrals in the fields of quantum mechanics and statistical physics. It is written for graduate students and researchers in physics, mathematical physics, applied mathematics as well as chemistry. The material is presented in an accessible manner for readers with little knowledge of quantum mechanics and no prior exposure to path integrals. It begins with elementary concepts and a review of quantum mechanics that gradually builds the framework for the Feynman path integrals and how they are applied to problems in quantum mechanics and statistical physics. Problem sets throughout the book allow readers to test their understanding and reinforce the explanations of the theory in real situations. Features: Comprehensive and rigorous yet, presents an easy-to-understand approach. Applicable to a wide range of disciplines. Accessible to those with little, or basic, mathematical understanding.

Author : M Chaichian,A Demichev
Publisher : CRC Press
Page : 359 pages
File Size : 54,8 Mb
Release : 2018-10-08
Category : Science
ISBN : 9781482268911

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Path Integrals in Physics by M Chaichian,A Demichev Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 50,7 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9789814469272

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Mathematical Feynman Path Integrals and Their Applications by Anonim Pdf

Author : Richard Phillips Feynman,Laurie M. Brown
Publisher : World Scientific
Page : 142 pages
File Size : 51,6 Mb
Release : 2005
Category : Science
ISBN : 9789812563668

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Feynman's Thesis by Richard Phillips Feynman,Laurie M. Brown Pdf

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.

Author : George J. Papadopoulos,J. T. Devreese
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 46,5 Mb
Release : 2013-11-11
Category : Science
ISBN : 9781468491401

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Path Integrals by George J. Papadopoulos,J. T. Devreese Pdf

The Advanced Study Institute on "Path Integrals and Their Applications in Quantum, Statistical, and Solid State Physics" was held at the University of Antwerpen (R.U.C.A.), July 17-30, 1977. The Institute was sponsored by NATO. Co-sponsors were: A.C.E.C. (Belgium), Agfa-Gevaert (Belgium), l'Air Li~uide BeIge (Belgium), Be1gonucleaire (Belgium), Bell Telephone Mfg. Co. (Belgium), Boelwerf (Belgium), Generale BankmaatschappiJ (Belgium), I.B.M. (Belgium), Kredietbank (Belgium), National Science Foundation (U.S.A.), Siemens (Belgium). A total of 100 lecturers and partici pants attended the Institute. The development of path (or functional) integrals in relation to problems of stochastic nature dates back to the early 20's. At that time, Wiener succeeded in obtaining the fundamental solution of the diffusion e~uation using Einstein's joint probability of finding a Brownian particle in a succession of space intervals during a corresponding succession of time intervals. Dirac in the early 30's sowed the seeds of the path integral formulation of ~uantum mecha nics. However, the major and decisive step in this direction was taken with Feynman's works in ~uantum and statistical physics, and quantum electrodynamicso The applications now extend to areas such as continuous mechanics, and recently functional integration methods have been employed by Edwards for the study of polymerized matter

Author : Stuart A. Rice
Publisher : John Wiley & Sons
Page : 0 pages
File Size : 46,8 Mb
Release : 2009-08-03
Category : Science
ISBN : 0470500255

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Advances in Chemical Physics, Volume 143 by Stuart A. Rice Pdf

The Advances in Chemical Physics series presents the cutting edge in every area of the discipline and provides the field with a forum for critical, authoritative evaluations of advances. It provides an editorial framework that makes each volume an excellent supplement to advanced graduate classes, with contributions from experts around the world and a handy glossary for easy reference on new terminology. This series is a wonderful guide for students and professionals in chemical physics and physical chemistry, from academia, government, and industries including chemicals, pharmaceuticals, and polymers.