Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets 4th Edition

Author : Hagen Kleinert
Publisher : World Scientific
Page : 1626 pages
File Size : 50,5 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 : Unknown
Page : 1593 pages
File Size : 45,6 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 : Hagen Kleinert
Publisher : World Scientific Publishing Company
Page : 1505 pages
File Size : 53,7 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
Page : 1592 pages
File Size : 44,7 Mb
Release : 2006-07-19
Category : Science
ISBN : 9789813101715

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

This is the fourth, 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.

Author : Kleinert Hagen
Publisher : World Scientific
Page : 1624 pages
File Size : 47,6 Mb
Release : 2009-05-18
Category : Science
ISBN : 9789814365260

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Path Integrals In Quantum Mechanics, Statistics, Polymer Physics, And Financial Markets (5th Edition) by Kleinert Hagen Pdf

This is the fifth, 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 been made possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's time-sliced formula to include singular attractive 1/r- and 1/r2-potentials. The second is a new nonholonomic mapping principle carrying physical laws in flat spacetime to spacetimes 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, coordinate-independent 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 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 results. The convergence is uniform from weak to strong couplings, opening a way to precise evaluations of analytically unsolvable path integrals in the strong-coupling regime where they describe critical phenomena.Tunneling processes are treated in detail, with applications to the lifetimes of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions. A variational treatment extends the range of validity to small barriers. A corresponding extension of the large-order perturbation theory now also applies to small orders.Special attention is devoted to path integrals with topological restrictions needed to understand 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, recently experienced in the world markets, that large fluctuations occur much more frequently than in Gaussian distributions.

Author : Hagen Kleinert
Publisher : World Scientific Publishing Company Incorporated
Page : 664 pages
File Size : 49,9 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 : Laskin Nick
Publisher : World Scientific
Page : 360 pages
File Size : 45,6 Mb
Release : 2018-05-25
Category : Science
ISBN : 9789813223813

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Fractional Quantum Mechanics by Laskin Nick Pdf

Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum physics. This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder. The fractional Schrödinger equation and the fractional path integral are new fundamental physical concepts introduced and elaborated in the book. The fractional Schrödinger equation is a manifestation of fractional quantum mechanics. The fractional path integral is a new mathematical tool based on integration over Lévy flights. The fractional path integral method enhances the well-known Feynman path integral framework. Related topics covered in the text include time fractional quantum mechanics, fractional statistical mechanics, fractional classical mechanics and the α-stable Lévy random process. The book is well-suited for theorists, pure and applied mathematicians, solid-state physicists, chemists, and others working with the Schrödinger equation, the path integral technique and applications of fractional calculus in various research areas. It is useful to skilled researchers as well as to graduate students looking for new ideas and advanced approaches.

Author : Wolfhard Janke,Axel Pelster
Publisher : World Scientific
Page : 629 pages
File Size : 52,8 Mb
Release : 2008
Category : Science
ISBN : 9789812837264

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Path Integrals by Wolfhard Janke,Axel Pelster Pdf

This proceedings volume contains selected talks and poster presentations from the 9th International Conference on Path Integrals ? New Trends and Perspectives, which took place at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, during the period September 23?28, 2007. Continuing the well-developed tradition of the conference series, the present status of both the different techniques of path integral calculations and their diverse applications to many fields of physics and chemistry is reviewed. This is reflected in the main topics in this volume, which range from more traditional fields such as general quantum physics and quantum or statistical field theory through technical aspects like Monte Carlo simulations to more modern applications in the realm of quantum gravity and astrophysics, condensed matter physics with topical subjects such as Bose?Einstein condensation or quantum wires, biophysics and econophysics. All articles are successfully tied together by the common method of path integration; as a result, special methodological advancements in one topic could be transferred to other topics.

Author : Ulrich Weiss
Publisher : World Scientific
Page : 588 pages
File Size : 42,5 Mb
Release : 2012-03-05
Category : Science
ISBN : 9789814452984

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Quantum Dissipative Systems by Ulrich Weiss Pdf

Starting from first principles, this book introduces the fundamental concepts and methods of dissipative quantum mechanics and explores related phenomena in condensed matter systems. Major experimental achievements in cooperation with theoretical advances have brightened the field and brought it to the attention of the general community in natural sciences. Nowadays, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book — originally published in 1990 and republished in 1999 and and 2008 as enlarged second and third editions — delves significantly deeper than ever before into the fundamental concepts, methods and applications of quantum dissipative systems. This fourth edition provides a self-contained and updated account of the quantum mechanics of open systems and offers important new material including the most recent developments. The subject matter has been expanded by about fifteen percent. Many chapters have been completely rewritten to better cater to both the needs of newcomers to the field and the requests of the advanced readership. Two chapters have been added that account for recent progress in the field. This book should be accessible to all graduate students in physics. Researchers will find this a rich and stimulating source. Contents:IntroductionGeneral Theory of Open Quantum Systems:Diverse Limited Approaches: A Brief SurveySystem-Plus-Reservoir ModelsImaginary-Time Approach and Equilibrium DynamicsReal-Time Path Integrals and Nonequilibrium DynamicsMiscellaneous Applications:Damped Linear Quantum Mechanical OscillatorQuantum Brownian Free MotionThe Thermodynamic Variational ApproachSuppression of Quantum CoherenceQuantum Statistical Decay:IntroductionClassical Rate Theory: A Brief OverviewQuantum Rate Theory: Basic Methods Multidimensional Quantum Rate TheoryCrossover From Thermal to Quantum DecayThermally Activated DecayThe Crossover RegionDissipative Quantum TunnelingThe Dissipative Two-State System:IntroductionThermodynamicsElectron Transfer and Incoherent TunnelingTwo-State Dynamics: Basics and MethodsTwo-State Dynamics: Sundry TopicsThe Driven Two-State SystemThe Dissipative Multi-State System:Quantum Brownian Particle in a Washboard PotentialMulti-State DynamicsDuality SymmetryTwisted Partition Function and Nonlinear MobilityCharge Transport in Quantum Impurity SystemsQuantum Transport for Sub- and Super-Ohmic Friction Readership: Advanced undergraduate and graduate students; researchers in quantum statistical and condensed matter physics, in quantum/classical mechanics, in quantum information and quantum state engineering, in quantum optics, and in Bose-condensed systems. Keywords:Quantum System;Quantum Tunneling;Quantum Mechanics;Thermodynamics

Author : Gregory S. Chirikjian,Alexander B. Kyatkin
Publisher : Courier Dover Publications
Page : 881 pages
File Size : 40,5 Mb
Release : 2016-07-20
Category : Mathematics
ISBN : 9780486795645

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Harmonic Analysis for Engineers and Applied Scientists by Gregory S. Chirikjian,Alexander B. Kyatkin Pdf

Although the Fourier transform is among engineering's most widely used mathematical tools, few engineers realize that the extension of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. This self-contained approach, geared toward readers with a standard background in engineering mathematics, explores the widest possible range of applications to fields such as robotics, mechanics, tomography, sensor calibration, estimation and control, liquid crystal analysis, and conformational statistics of macromolecules. Harmonic analysis is explored in terms of particular Lie groups, and the text deals with only a limited number of proofs, focusing instead on specific applications and fundamental mathematical results. Forming a bridge between pure mathematics and the challenges of modern engineering, this updated and expanded volume offers a concrete, accessible treatment that places the general theory in the context of specific groups.

Author : Gert Roepstorff
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642578861

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Path Integral Approach to Quantum Physics by Gert Roepstorff Pdf

Specifically designed to introduce graduate students to the functional integration method in contemporary physics as painlessly as possible, the book concentrates on the conceptual problems inherent in the path integral formalism. Throughout, the striking interplay between stochastic processes, statistical physics and quantum mechanics comes to the fore, and all the methods of fundamental interest are generously illustrated by important physical examples.

Author : Lukong Cornelius Fai
Publisher : CRC Press
Page : 415 pages
File Size : 43,8 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 : Lev Kantorovich
Publisher : Springer Nature
Page : 944 pages
File Size : 42,5 Mb
Release : 2023
Category : Chemometrics
ISBN : 9783031463204

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Mathematics for Natural Scientists by Lev Kantorovich Pdf

This textbook, the second in a series (the first covered fundamentals and basics), seeks to make its material accessible to physics students. Physics/engineering can be greatly enhanced by knowledge of advanced mathematical techniques, but the math-specific jargon and laborious proofs can be off-putting to students not well versed in abstract math. This book uses examples and proofs designed to be clear and convincing from the context of physics, as well as providing a large number of both solved and unsolved problems in each chapter. This is the second edition, and it has been significantly revised and enlarged, with Chapters 1 (on linear algebra) and 2 (on the calculus of complex numbers and functions) having been particularly expanded. The enhanced topics throughout the book include: vector spaces, general (non-Hermitian, including normal and defective) matrices and their right/left eigenvectors/values, Jordan form, pseudoinverse, linear systems of differential equations, Gaussian elimination, fundamental theorem of algebra, convergence of a Fourie series and Gibbs-Wilbraham phenomenon, careful derivation of the Fourier integral and of the inverse Laplace transform. New material has been added on many physics topics meant to illustrate the maths, such as 3D rotation, properties of the free electron gas, van Hove singularities, and methods for both solving PDEs with a Fourier transform and calculating the width of a domain wall in a ferromagnet, to mention just a few. This textbook should prove invaluable to all of those with an interest in physics/engineering who have previously experienced difficulty processing the math involved. .

Author : Rainer Dick
Publisher : Springer Science & Business Media
Page : 558 pages
File Size : 54,7 Mb
Release : 2012-01-10
Category : Science
ISBN : 9781441980762

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Advanced Quantum Mechanics by Rainer Dick Pdf

This book introduces quantum mechanics from the discovery of photons to field quantization, relativistic quantum fields and photon-matter interactions. It emphasizes the role of quantum theory for an understanding of materials and electromagnetic radiation.

Author : George J. Papadopoulos,J. T. Devreese
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 44,7 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