This textbook on the theory and applications of path integrals contains the solution to a number of non-trivial path integrals, most notably that of the Coulomb system. This has become possible by finding a consistent formulation of path integrals in spaces with curvature and torsion. Special emphasis is given to stability problems of path fluctuations in the presence of singular potentials such as centrifugal and angular barriers. The limitations of Feynman's time slicing procedure are exhibited and a new path integral formula is found which avoids the frequent danger of path collapse. The physically important applications to tunnelling problems are analyzed in detail. Their relevance to superconductivity and the large-order behaviour of perturbation expansions is demonstrated. The path integral description of equilibrium thermodynamics is presented, and an extension to non-equilibrium processes is presented. Much attention is paid to path integrals in spaces with topological restrictions. Their applications to entanglement problems in polymer physics and their relevance to particle statistics are discussed, also to the recently popular phenomenon of fractional statistics. Now in its second edition, the book has been extended by a more powerful variational approach which can now be applied to excited states and to tunnelling processes through high as well as low barriers. With it, the known large-order perturbation theory has been continued down to small orders. The book contains a detailed non-abelian Chern-Simons theory of polymer entanglement in terms of HOMFLY-polynomials and a discussion of anyonic aspects of the fractional quantum Hall effect and of high-Tc superconductivity. The semiclassical analysis incorporates now multidimensional systems to establish contact with recent work on chaos.
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Editorial Reviews
Review
Kleinert's book presents the reader with a very complete and very thorough discussion of path integration... -- Journal of Statistical Physics, Apr 2003
--This text refers to the
Hardcover
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About the Author
Hagen Kleinert is Professor of Physics at the Freie Universität Berlin, Germany. As a visiting scientist, he has spent extended periods of time at CERN, the European Organization for Nuclear Research in Geneva; at the California Institute of Technology in Pasadena; at the Universities of California in Berkeley, Santa Barbara, and San Diego; at the Los Alamos National Laboratories in New Mexico; and at Princeton University, New Jersey. He has made numerous contributions to our understanding of particle physics, mathematical physics, condensed matter physics, chemical physics, and nuclear physics. His two-volume book Gauge Fields in Condensed Matter, published by World Scientific, develops a new quantum field-theory of phase transitions on the basis of disorder fields. Such fields have since become a powerful tool to investigate the statistical properties of fluctuating line-like excitations in various many-body systems such as superfluids, superconductors, and crystals.
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12 of 13 people found the following review helpful:
5.0 out of 5 stars
Kleinerts Completeness,
This review is from: Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (Paperback)
Kleinerts book "Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics" presents the reader with a very complete and very thorough discussion of path integration. The book offers such a wealth of topics,it becomes straightforward to select material, both for advanced undergraduate as well as graduate courses in theoretical physics.Many, many issues dealt with in this volume have appeared here for the first time, such as the inclucion of the quantum mechanics of the hydrogen atom through path integrals. This book is a major step towards bringing this approach to quantum physics onto the same educational footing as the Schrödinger equation that standard texts focus on. This book profits from the clarity and conciseness that is also a hallmark of Kleinerts scientific papers. I would say this volume is highly recommendable for any student considering to major in {theoretical} physics, and an absolute must for any lecturer in this area. Infact, I don't know of any excuse not to have your own copy.
5 of 6 people found the following review helpful:
5.0 out of 5 stars
One of The only TWO Books to own on PI's,
By Tim H (New York, NY United States) - See all my reviews
This review is from: Path Integrals in Quantum Mechanics Statistics and Polymer Physics (Paperback)
Kleinert the physicist is NOTHING short of phenomenal. This book is just one of his many treatises. After reading Feynman(+Hibbs) this is the text to follow up.
Sadly the second edition which is in print contain MANY typos. The third edition fixes much if not all, so skip right onto the 3rd or higher edition.
5 of 15 people found the following review helpful:
5.0 out of 5 stars
i liked it,
By chicken head cut off "mcscientist" (Gainesville/Orsay France) - See all my reviews
This review is from: Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics, and Financial Markets, Third Edition (Paperback)
So a little background on Kleinert: feynman could NOT solve the schrodinger equation with the path integral and kleinert, using some group theoretical methods did. or so that's what i was told.His book reflects that. This book is full of interesting facts that arent elsewhere.
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
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The orbits of a classical-mechanical system are described by a set of time-dependent generalized coordinates q1(t), . . . , qN(t). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
effective classical potential, variational perturbation expansion, nonholonomic mapping, sliced action, sliced time axis, smearing formula, time evolution amplitude, radial path integral, watermelon diagrams, increasing dash length, irreducible vacuum diagrams, fundamental composition law, smeared potential, variational interpolation, physical scalar product, effective classical action, variational perturbation theory, quadratic completion, inhomogeneous field equation, ambiguous integrals, fluctuation determinant, angular barrier, commuting derivatives, nonholonomic transformation, coinciding endpoints Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, World Scientific, Monte Carlo, Nuovo Cimento, Condensed Matter, John Wiley, Cambridge University Press, Theoretical Physics, Van Vleck-Pauli-Morette, Low Temp, Pergamon Press, Hilbert Space of Quantized Grassmann Variable, Lecture Notes, Fluctuating Bose Fields, Plenum Press, Princeton University Press, Academic Press, Calculation of Perturbation Series, Classical Motion of Mass Point, Combining Eqs, Large-x Behavior of Truncated, Path Integral Coupled, Solid State Communs, Systematic Improvement of Feynman-Kleinert Approximation, The Mathematica New!
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
The orbits of a classical-mechanical system are described by a set of time-dependent generalized coordinates q1(t), . . . , qN(t). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
effective classical potential, variational perturbation expansion, nonholonomic mapping, sliced action, sliced time axis, smearing formula, time evolution amplitude, radial path integral, watermelon diagrams, increasing dash length, irreducible vacuum diagrams, fundamental composition law, smeared potential, variational interpolation, physical scalar product, effective classical action, variational perturbation theory, quadratic completion, inhomogeneous field equation, ambiguous integrals, fluctuation determinant, angular barrier, commuting derivatives, nonholonomic transformation, coinciding endpoints Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, World Scientific, Monte Carlo, Nuovo Cimento, Condensed Matter, John Wiley, Cambridge University Press, Theoretical Physics, Van Vleck-Pauli-Morette, Low Temp, Pergamon Press, Hilbert Space of Quantized Grassmann Variable, Lecture Notes, Fluctuating Bose Fields, Plenum Press, Princeton University Press, Academic Press, Calculation of Perturbation Series, Classical Motion of Mass Point, Combining Eqs, Large-x Behavior of Truncated, Path Integral Coupled, Solid State Communs, Systematic Improvement of Feynman-Kleinert Approximation, The Mathematica New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
8
books
cite this book:
See all 8 books citing this book
- Critical Properties of o4 Theories by Kleinert Hagen on page 426
- Advances in Imaging and Electron Physics, Volume 110 (Srlances in Imaging & Electron Physics) by Peter W. Hawkes on page 170
- Introduction to Quantum Field Theory by V.lG. Kiselev in Front Matter
- Soft Condensed Matter Physics in Molecular and Cell Biology (Scottish Graduate Series) by W.C.K. Poon on page 199
- Computer Simulation Studies in Condensed-Matter Physics XVII: Proceedings of the Seventeenth Workshop, Athens, GA, USA, February 16-20, 2004 (Springer Proceedings in Physics) (v. 17) by David P. Landau on page 195
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