Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets

Author : Hagen Kleinert
Publisher : World Scientific
Page : 1626 pages
File Size : 43,9 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
Page : 1505 pages
File Size : 48,6 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 : Unknown
Page : 1593 pages
File Size : 48,8 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 Incorporated
Page : 891 pages
File Size : 44,6 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 : R. J. Rivers
Publisher : Cambridge University Press
Page : 356 pages
File Size : 51,5 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 : Belal E. Baaquie
Publisher : Cambridge University Press
Page : 334 pages
File Size : 53,5 Mb
Release : 2007-07-23
Category : Business & Economics
ISBN : 9781139456395

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Quantum Finance by Belal E. Baaquie Pdf

This book applies the mathematics and concepts of quantum mechanics and quantum field theory to the modelling of interest rates and the theory of options. Particular emphasis is placed on path integrals and Hamiltonians. Financial mathematics is dominated by stochastic calculus. The present book offers a formulation that is completely independent of that approach. As such many results emerge from the ideas developed by the author. This work will be of interest to physicists and mathematicians working in the field of finance, to quantitative analysts in banks and finance firms and to practitioners in the field of fixed income securities and foreign exchange. The book can also be used as a graduate text for courses in financial physics and financial mathematics.

Author : Asim O. Barut,Wesley E. Brittin
Publisher : Unknown
Page : 458 pages
File Size : 50,5 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 : Richard Phillips Feynman,Laurie M. Brown
Publisher : World Scientific
Page : 142 pages
File Size : 48,5 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 : Hagen Kleinert
Publisher : World Scientific
Page : 1512 pages
File Size : 47,5 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 : Hagen Kleinert
Publisher : World Scientific Publishing Company Incorporated
Page : 664 pages
File Size : 43,6 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 : Andreas Wipf
Publisher : Springer Nature
Page : 568 pages
File Size : 55,7 Mb
Release : 2021-10-25
Category : Science
ISBN : 9783030832636

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Statistical Approach to Quantum Field Theory by Andreas Wipf Pdf

This new expanded second edition has been totally revised and corrected. The reader finds two complete new chapters. One covers the exact solution of the finite temperature Schwinger model with periodic boundary conditions. This simple model supports instanton solutions – similarly as QCD – and allows for a detailed discussion of topological sectors in gauge theories, the anomaly-induced breaking of chiral symmetry and the intriguing role of fermionic zero modes. The other new chapter is devoted to interacting fermions at finite fermion density and finite temperature. Such low-dimensional models are used to describe long-energy properties of Dirac-type materials in condensed matter physics. The large-N solutions of the Gross-Neveu, Nambu-Jona-Lasinio and Thirring models are presented in great detail, where N denotes the number of fermion flavors. Towards the end of the book corrections to the large-N solution and simulation results of a finite number of fermion flavors are presented. Further problems are added at the end of each chapter in order to guide the reader to a deeper understanding of the presented topics. This book is meant for advanced students and young researchers who want to acquire the necessary tools and experience to produce research results in the statistical approach to Quantum Field Theory.

Author : Edward L. Wolf
Publisher : John Wiley & Sons
Page : 336 pages
File Size : 46,6 Mb
Release : 2015-08-04
Category : Technology & Engineering
ISBN : 9783527684182

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Nanophysics and Nanotechnology by Edward L. Wolf Pdf

Long awaited new edition of this highly successful textbook, provides once more a unique introduction to the concepts, techniques and applications of nanoscale systems by covering its entire spectrum up to recent findings on graphene.

Author : RAINER DICK
Publisher : Springer
Page : 692 pages
File Size : 47,7 Mb
Release : 2016-07-01
Category : Science
ISBN : 9783319256757

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Advanced Quantum Mechanics by RAINER DICK Pdf

In this updated and expanded second edition of a well-received and invaluable textbook, Prof. Dick emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. Advanced Quantum Mechanics, Materials and Photons can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible Appendices A and B also provide introductions to Lagrangian mechanics and the covariant formulation of electrodynamics. This second edition includes an additional 62 new problems as well as expanded sections on relativistic quantum fields and applications of quantum electrodynamics. Other special features include an introduction to Lagrangian field theory and an integrated discussion of transition amplitudes with discrete or continuous initial or final states. Once students have acquired an understanding of basic quantum mechanics and classical field theory, canonical field quantization is easy. Furthermore, the integrated discussion of transition amplitudes naturally leads to the notions of transition probabilities, decay rates, absorption cross sections and scattering cross sections, which are important for all experimental techniques that use photon probes.

Author : Alexei A. Maradudin
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 43,5 Mb
Release : 2010-05-10
Category : Science
ISBN : 9780387356594

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Light Scattering and Nanoscale Surface Roughness by Alexei A. Maradudin Pdf

This book covers both experimental and theoretical aspects of nanoscale light scattering and surface roughness. Topics include: spherical particles located on a substrate; surface and buried interface roughness; surface roughness of polymer thin films; magnetic and thermal fluctuations at planar surfaces; speckle patterns; scattering of electromagnetic waves from a metal; multiple wavelength light scattering; nanoroughness standards.

Author : Marvin L. Cohen,James R. Chelikowsky
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642613388

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Electronic Structure and Optical Properties of Semiconductors by Marvin L. Cohen,James R. Chelikowsky Pdf