Path Integrals in Quantum Mechanics, Statistics and Polymer Physics / Edition 2

Path Integrals in Quantum Mechanics, Statistics and Polymer Physics / Edition 2

by Hagen Kleinert, Hagen Kleinart
     
 

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… See more details below

Overview

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/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. 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.

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Product Details

ISBN-13:
9789810214722
Publisher:
World Scientific Publishing Company, Incorporated
Publication date:
06/01/1995
Pages:
800
Product dimensions:
6.03(w) x 8.50(h) x 1.66(d)

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Table of Contents

1Fundamentals1
2Path Integrals - Elementary Properties and Simple Solutions67
3External Sources, Correlations, and Perturbation Theory147
4Semiclassical Time Evolution Amplitude199
5Variational Perturbation Theory229
6Path Integrals with Topological Constraints297
7Many Particle Orbits - Statistics and Second Quantization311
8Path Integrals in Spherical Coordinates343
9Fixed-Energy Amplitude and Wave Functions395
10Short-Time Amplitude in Spaces with Curvature and Torsion419
11Schrodinger Equation in General Metric-Affine Spaces449
12New Path Integral Formula for Singular Potentials471
13Path Integral of the Coulomb System485
14Solution of Further Path Integrals by the Duru-Kleinert Method529
15Path Integrals in Polymer Physics578
16Polymers and Particle Orbits in Multiply Connected Spaces615
17Path Integrals and Tunneling692
18Path Integrals and Nonequilibrium Quantum Statistics797
19Path Integrals for Relativistic Particle Orbits848
Index861

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