Mathematical Feynman Path Integrals And Their Applications PDF Download
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Author | : Sonia Mazzucchi |
Publisher | : World Scientific |
Total Pages | : 360 |
Release | : 2021-11-16 |
Genre | : Science |
ISBN | : 9811214808 |
Download Mathematical Feynman Path Integrals And Their Applications (Second Edition) Book in PDF, ePub and Kindle
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.
Author | : Sergio A. Albeverio |
Publisher | : Springer |
Total Pages | : 143 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 354038250X |
Download Mathematical Theory of Feynman Path Integrals Book in PDF, ePub and Kindle
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.
Author | : L. S. Schulman |
Publisher | : Courier Corporation |
Total Pages | : 434 |
Release | : 2012-10-10 |
Genre | : Science |
ISBN | : 0486137023 |
Download Techniques and Applications of Path Integration Book in PDF, ePub and Kindle
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.
Author | : Sergio Albeverio |
Publisher | : Springer |
Total Pages | : 184 |
Release | : 2008-05-06 |
Genre | : Mathematics |
ISBN | : 3540769560 |
Download Mathematical Theory of Feynman Path Integrals Book in PDF, ePub and Kindle
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.
Author | : Richard Phillips Feynman |
Publisher | : |
Total Pages | : 0 |
Release | : 1965 |
Genre | : Quantum theory |
ISBN | : 9780071139489 |
Download Quantum Mechanics and Path Integrals [by] R.P. Feynman [and] A.R. Hibbs Book in PDF, ePub and Kindle
Author | : |
Publisher | : Allied Publishers |
Total Pages | : 364 |
Release | : 2002 |
Genre | : |
ISBN | : 9788177642315 |
Download Path-integral methods and their applications Book in PDF, ePub and Kindle
Author | : Hagen Kleinert |
Publisher | : World Scientific |
Total Pages | : 1512 |
Release | : 2004 |
Genre | : Science |
ISBN | : 9789812381071 |
Download Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets Book in PDF, ePub and Kindle
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 | : Horacio S. Wio |
Publisher | : World Scientific |
Total Pages | : 174 |
Release | : 2013 |
Genre | : Mathematics |
ISBN | : 9814449040 |
Download Path Integrals for Stochastic Processes Book in PDF, ePub and Kindle
This book provides an introductory albeit solid presentation of path integration techniques as applied to the field of stochastic processes. The subject began with the work of Wiener during the 1920''s, corresponding to a sum over random trajectories, anticipating by two decades Feynman''s famous work on the path integral representation of quantum mechanics. However, the true trigger for the application of these techniques within nonequilibrium statistical mechanics and stochastic processes was the work of Onsager and Machlup in the early 1950''s. The last quarter of the 20th century has witnessed a growing interest in this technique and its application in several branches of research, even outside physics (for instance, in economy).The aim of this book is to offer a brief but complete presentation of the path integral approach to stochastic processes. It could be used as an advanced textbook for graduate students and even ambitious undergraduates in physics. It describes how to apply these techniques for both Markov and non-Markov processes. The path expansion (or semiclassical approximation) is discussed and adapted to the stochastic context. Also, some examples of nonlinear transformations and some applications are discussed, as well as examples of rather unusual applications. An extensive bibliography is included. The book is detailed enough to capture the interest of the curious reader, and complete enough to provide a solid background to explore the research literature and start exploiting the learned material in real situations.
Author | : Mark S. Swanson |
Publisher | : Courier Corporation |
Total Pages | : 463 |
Release | : 2014-02-19 |
Genre | : Science |
ISBN | : 0486782301 |
Download Path Integrals and Quantum Processes Book in PDF, ePub and Kindle
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.
Author | : George J. Papadopoulos |
Publisher | : Springer Science & Business Media |
Total Pages | : 516 |
Release | : 2013-11-11 |
Genre | : Science |
ISBN | : 1468491407 |
Download Path Integrals Book in PDF, ePub and Kindle
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