Path Integrals In Quantum Mechanics, Statistics, And Polymer Physics (2nd Edition)

Hagen Kleinert

ISBN 10: 9810214715 / ISBN 13: 9789810214715

Published by World Scientific Publishing Co Pte Ltd, 1995

About this Item

Ancien livre de bibliothèque. Couverture différente. Edition 1995. Ammareal reverse jusqu'à 15% du prix net de cet article à des organisations caritatives. ENGLISH DESCRIPTION Book Condition: Used, Very good. Former library book. Different cover. Edition 1995. Ammareal gives back up to 15% of this item's net price to charity organizations.

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Bibliographic Details

• Title: Path Integrals In Quantum Mechanics, Statistics, And Polymer Physics (2nd Edition)
• Publisher: World Scientific Publishing Co Pte Ltd
• Publication Date: 1995
• Language: English
• ISBN 10: 9810214715
• ISBN 13: 9789810214715
• Binding: Hardcover
• Edition: 2nd Edition
• Condition: Très bon

About this title

Synopsis

This is the second, significantly expanded edition of the comprehensive textbook of 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 of 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 famous formula to include singular 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.The powerful Feynman-Kleinert variational approach is explained and developed systematically into a variational perturbation expansion. In contrast to ordinary perturbation expansions, divergencies are absent. Instead, there is a uniform convergence 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 now also applies 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.

Review

"Kleinert's book presents the reader with a very complete and very thorough discussion of path integration... a new extensive and, again, rather complete chapter has been added on the use of path integration techniques in the analysis of financial markets. This chapter would do well in any high-level course on stochastic financial models and is a wonderful occasion for candidate mathematical and theoretical physicists to realize what great potential there hides still in the methodologies and techniques that have been developed... It profits from the clarity and conciseness that is also a hallmark of Kleinert's scientific papers... this volume is highly recommendable for any student considering majoring in theoretical physics or chemistry, and an absolute must for any lecturer in this area... In fact, I don't know of any excuse not to have your own copy." Journal of Statistical Physics, Apr 2003"