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Path Integrals in Quantum Mechanics, Statistics, Polymer Physicsnd Financial Markets (3rd Edition) / Edition 3

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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: 9789812381064
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 3/5/2004
  • Edition description: Expanded
  • Edition number: 3
  • Pages: 1468
  • Product dimensions: 6.24 (w) x 9.26 (h) x 0.75 (d)

Table of Contents

1 Fundamentals 1
2 Path integrals - elementary properties and simple solutions 77
3 External sources, correlations, and perturbation theory 187
4 Semiclassical time evolution amplitude 332
5 Variational perturbation theory 403
6 Path integrals with topological constraints 532
7 Many particle orbits - statistics and second quantization 553
8 Path integrals in spherical coordinates 646
9 Fixed-energy amplitude and wave functions 693
10 Spaces with curvature and torsion 715
11 Schrodinger equation in general metric-affine spaces 843
12 New path integral formula for singular potentials 867
13 Path integral of Coulomb system 880
14 Solution of further path integrals by the Duru-Kleinert method 925
15 Path integrals in polymer physics 969
16 Polymers and particle orbits in multiply connected spaces 1018
17 Tunneling 1103
18 Nonequilibrium quantum statistics 1203
19 Relativistic particle orbits 1303
20 Path integrals and financial markets 1342
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