Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial MarketsWorld Scientific, 2004 - Всего страниц: 1468 This is the third, significantly 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 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 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 Chem-Simons theory of particles with fractional statistics (anyohs) 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. |
Результаты поиска по книге
Результаты 1 – 5 из 93
... Effective Action by Loop Expansion Quadratic Fluctuations 3.19.3 . Effective Action to Second Order in ħ 273 . 273 278 . 281 . 3.20 3.19.4 Background Field Method for Effective Action Nambu - Goldstone Theorem 284 . 287 . 3.21 Effective ...
... Effective Classical Partition Function . . . 403 5.2 Local Harmonic Trial Partition Function . 404 5.3 Optimal Upper Bound .. 409 5.4 Accuracy of Variational Approximation 410 5.5 Weakly Bound Ground State Energy in Finite - Range ...
... Effective potential for w2 > 0 and w2 < 0 in mean - field approximation276 3.14 Local fluctuation width of harmonic oscillator 3.15 Plot of reduced Feynman integrals â ( x ) 4.1 Solution for screening function f ( ) in Thomas - Fermi ...
Извините, доступ к содержанию этой страницы ограничен..
Извините, доступ к содержанию этой страницы ограничен..
Содержание
Fundamentals | 1 |
External Sources Correlations and Perturbation Theory | 3 |
Appendix 1A The Asymmetric | 74 |
6 | 104 |
85 | 108 |
8 | 114 |
3 | 128 |
4 | 144 |
Point Particle on Circle | 532 |
3 | 541 |
551 | |
Notes and References | 642 |
FixedEnergy Amplitude and Wave Functions | 693 |
3 | 699 |
4 | 705 |
Notes and References | 714 |
5 | 159 |
Appendix 2A Derivation of BakerCampbellHausdorff and Magnus For | 179 |
3 | 187 |
Subtracted periodic Green function GP T 1w and antiperiodic | 198 |
87 | 199 |
6 | 236 |
14 | 243 |
8 | 257 |
Quadratic Fluctuations | 273 |
20 | 284 |
Energy Levels | 303 |
Appendix 3A Feynman Integrals for T 0 | 315 |
Semiclassical Time Evolution Amplitude | 332 |
4 | 349 |
8 | 355 |
9 | 365 |
11 | 387 |
3 | 392 |
Notes and References | 400 |
Appendix 5A Feynman Integrals for T0 without Zero Frequency | 510 |
5 | 742 |
7 | 750 |
Distributions as Limits of Bessel Function | 762 |
Schrödinger Equation in General MetricAffine Spaces | 843 |
New Path Integral Formula for Singular Potentials | 867 |
Path Integral of Coulomb System | 880 |
Solution of Further Path Integrals by the DuruKleinert Method | 925 |
Path Integrals in Polymer Physics | 969 |
Polymers and Particle Orbits in Multiply Connected Spaces | 1018 |
Tunneling | 1103 |
Appendix 17A Feynman Integrals for Fluctuation Correction | 1197 |
Nonequilibrium Quantum Statistics | 1203 |
5 | 1213 |
Relativistic Particle Orbits | 1303 |
Path Integrals and Financial Markets | 1342 |
Meixner Distributions | 1355 |
Tail Behavior for all Times | 1382 |
Appendix 20A Largex Behavior of Truncated Lévy Distribution | 1403 |
Notes and References | 1409 |
Другие издания - Просмотреть все
Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and ... Hagen Kleinert Ограниченный просмотр - 2004 |
Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and ... Hagen Kleinert Недоступно для просмотра - 2004 |