Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets 5th Edition by Hagen Kleinert | (PDF) Free Download

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Dear ReadersAnd just exactly how accurate are they in predicting economic trends………………???According to latest downturn in the economy circa 2008 at the end of G.W. Bush’s term and later, not veryunless they’re running two sets of books.This is going to take a while.But the task is not hopeless.One of the strangest and at the time most difficult topics I ever tried to understand. Path Integrals. Actually a part of what’s called “Functional Analysis”. But now after some “miraculous conversion” which has taken place in my psyche these path integrals seem not so bad after all. What has happened to change this? Several factors. Actually quite a few. This book of course is certainly the definitive textbook/research manual/”Bible” if there ever was one.To some new notation can be a formidable task to incorporate or get used to. At least for me it often is. Then add to that the conceptual difficulties when you tell someone “now integrate over all paths”.One’s mind protests:” What do you mean all paths?”Well you take path number one integrate that get an answer then multiply that by dx2 then integrate that then get an answer then multiply by dx3 intergrate then get an answer then generalize to dx(n) ( the n-th integral) get an answer then take the limit as n goes to infinity. Easy!”Then you say:”Yeah. Easy for you to say buddy. What the hell are all these paths for?””Well, their all contribute to the “action””Yeah, what action is that?””Well you know the Lagrangian”.”The what?””That’s right the Lagrangian. Kinetic Energy minus potental energy in this case all taken to be in the exponent of the natural log e and multiplied by the complex number , the root of minus oneBest RegardsSouthern Jameson Westp.s…….for financial markets they couldn’t have helped that much……… is that what they call the “best and the brightest”…….???

⭐Though I haven’t read very much of this enormous tome, I like the idea of reading it (some day). Kleinert has been extremely thorough here, and his expository style is excellent. One word of caution: if you’re mathematically oriented and are looking for a rigorous foundation of functional integration of the kind used in Feynman’s approach to quantum mechanics, you won’t find it here. This book concerns itself more with explaining and displaying the many uses of path integration, than with the foundations of the subject. That said, I highly recommend this fascinating book.

⭐Much more detail about path integrals than I expected. I wouldn’t want it as a first book.

⭐This is an excellent book for people who already know a little of the issue of path integrals, but for someone Neophyte be difficult to understand.Its applications are excellent.

⭐This is absolutely a great work for therectical physicists in current time who are interested in various aspects of applications of an important tool of mathematical physics.

⭐It’s a great book, and I plan to get it soon. But this current fifth edition seems to have many typographic mistakes and spelling errors – These are usually not important, except when the author writes a q when it should be q-dot (dq/dt).

⭐For me this book is like an encyclopedia of path integrals as it is the most comprehensive treatment of the subjects I have seen. I was shocked by the size of 1,500 pages. The level is at a graduate text, the style is heuristic, and the mathematics is done the way most welcomed by physicists and engineers.Naturally, this book is not meant to be read from the beginning to the end page by page. I did not see a “How to Use This Book” flowchart in the book though. The new 4th edition covers more semi-classical material in Chapter 4 but still does not include the Herman-Kluk propagator which has been studied a lot in the past few years especially by chemical physicists. Perturbation theory and Feynman diagrams are well presented. Spin and relativistic quantum mechanics are nicely treated. Two strong chapters are dedicated to polymer physics but Flory’s theory is only briefly discussed. The last chapter, ca. 70 pages, is all about finance as the title concludes with.Overall I give a 4-start for this very competent book, I believe that researchers would need to refer to the pages from time to time as a reference work. The author lists several very informative URLs in the book, e.g. links to useful computer codes, that really makes the book a great buy at a price of $38.

⭐It is an excellent review covering an extremely wide range of subjects by a world expert. The only complaint: it is too bulky.

⭐Great book, very useful for me.

⭐Recebi a poucos dias e não posso fazer avaliação do conteúdo. É um livro de 1500 páginas e, dessa forma, levarei bastante tempo para lê-lo.Das sollte eigentlich nicht passieren: das Buch wurde eingescannt, schlechterdings einer miserablen OCR-Erkennung unterzogen und dann ohne die geringste Rezension zum Kauf angeboten.Auf jeder Seite findet man drei, vier haarsträubende Buchstaben-Kombinationen, die ein ums andere Mal den gesamten Inhalt der Passagen unkenntlich machen.In dieser Form hat das Buch in einer vom Anspruch qualitativ hochwertigen digitalen Bibliothek nichts verloren!Klassiker unter den Quantenmechanikbuechern. Bestes Buch ueber Pfadintegrale!If you really need to study or research PI this is the book. It has all of it. The math is very thick but has to be.

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