Path Integrals in Quantum Mechanics, Statistics, Polymer Physicsnd Financial Markets (5th Edition) / Edition 5

Path Integrals in Quantum Mechanics, Statistics, Polymer Physicsnd Financial Markets (5th Edition) / Edition 5

by Hagen Kleinert
     
 

"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 become possible by two major advances. The first is a new

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Overview

"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 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/r[superscript 2] 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 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." 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.

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Product Details

ISBN-13:
9789814273558
Publisher:
World Scientific Publishing Company, Incorporated
Publication date:
07/28/2009
Edition description:
New Edition
Pages:
1579
Product dimensions:
5.80(w) x 9.10(h) x 2.30(d)

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Table of Contents

1Fundamentals1
2Path integrals - elementary properties and simple solutions77
3External sources, correlations, and perturbation theory187
4Semiclassical time evolution amplitude332
5Variational perturbation theory403
6Path integrals with topological constraints532
7Many particle orbits - statistics and second quantization553
8Path integrals in spherical coordinates646
9Fixed-energy amplitude and wave functions693
10Spaces with curvature and torsion715
11Schrodinger equation in general metric-affine spaces843
12New path integral formula for singular potentials867
13Path integral of Coulomb system880
14Solution of further path integrals by the Duru-Kleinert method925
15Path integrals in polymer physics969
16Polymers and particle orbits in multiply connected spaces1018
17Tunneling1103
18Nonequilibrium quantum statistics1203
19Relativistic particle orbits1303
20Path integrals and financial markets1342

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