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Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets [Hardcover]

By Hagen Kleinert (Author)
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Item description for Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets by Hagen Kleinert...

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 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.

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Item Specifications...

Studio: World Scientific Publishing Company
Pages   1592
Est. Packaging Dimensions:   Length: 10.2" Width: 7.4" Height: 2.3"
Weight:   5.85 lbs.
Binding  Hardcover
Release Date   Jul 19, 2006
Publisher   World Scientific Publishing Company
ISBN  9812700080  
ISBN13  9789812700087  

Availability  0 units.

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Reviews - What do customers think about Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets?

Very good book  May 13, 2008
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.
A Phenomenal Treatise  Nov 16, 2006
Kleinert's work is NOTHING short of phenomenal.
After reading Feynman(+Hibbs) this is the text to follow up.

Sadly the second edition which is in print contained MANY typos.
The third edition fixes much, if not all; it also has added many new topics of various interest.

The core physics remains as solid, and even clearer than the previous editions.

Without casting aspersions on the presentation:
Make no mistake; this is no comic book.
You will suffer, scrape your gyri, and bruise your ego, but will be justly rewarded for your effort in study.

Consider this an unqualified recommendation.

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