Title
PATH INTEGRALS IN QUANTUM MECHANICS, STATISTICS, POLYMER PHYSICS, AND FINANCIAL MARKETS (5TH EDITION),Used
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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 quantummechanical systems, in particular 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 timesliced formula to include singular attractive 1/r and 1/r2potentials. The second is a new nonholonomic mapping principle carrying physical laws in flat spacetime to spacetimes with curvature and torsion, which leads to timesliced path integrals that are manifestly invariant under coordinate transformations. In addition to the timesliced definition, the author gives a perturbative, coordinateindependent 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 products of distributions. The powerful FeynmanKleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent results. The convergence is uniform from weak to strong couplings, opening a way to precise evaluations of analytically unsolvable path integrals in the strongcoupling regime where they describe critical phenomena.Tunneling processes are treated in detail, with applications to the lifetimes of supercurrents, the stability of metastable thermodynamic phases, and the largeorder behavior of perturbation expansions. A variational treatment extends the range of validity to small barriers. A corresponding extension of the largeorder perturbation theory now also applies to small orders.Special attention is devoted to path integrals with topological restrictions needed to understand the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The ChernSimons 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 BlackScholes formula for option prices are developed which account for the fact, recently experienced in the world markets, that large fluctuations occur much more frequently than in Gaussian distributions.
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- Q: What is the focus of the book 'Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets'? A: The book focuses on the theory and applications of path integrals, particularly in quantum mechanics, polymer physics, and financial markets. It covers a variety of nontrivial quantum-mechanical systems, emphasizing the hydrogen atom and various applications in different fields.
- Q: Who is the author of this book and what is his background? A: The author of the book is Hagen Kleinert, a renowned physicist known for his work in theoretical physics, particularly in the areas of path integrals and statistical mechanics.
- Q: What are the key features of this 5th edition of the book? A: This 5th edition is expanded and includes new formulations of path integrals, a systematic development of variational perturbation theory, and discussions on tunneling processes, statistical properties of particles, and financial market applications.
- Q: How many pages does the book contain? A: The book contains a total of 1624 pages, making it a comprehensive resource for its topics.
- Q: Is this book suitable for beginners in quantum mechanics? A: While this book provides in-depth explanations and advanced theoretical concepts, it may be more suitable for readers with a foundational understanding of quantum mechanics and mathematics.
- Q: What is the binding type of the book? A: The book is available in paperback binding, which is lightweight and flexible, making it easy to handle and read.
- Q: Can this book be used for research purposes? A: Yes, this book is a valuable resource for researchers in physics, finance, and related fields, providing theoretical insights and applications relevant to various advanced topics.
- Q: What is the condition of the book being sold? A: The book is listed as 'Used Book in Good Condition', indicating it may have some signs of wear but is still functional and usable.
- Q: What notable theories are discussed in this book? A: The book discusses several notable theories, including the Feynman-Kleinert variational approach, Chern-Simons theory, and applications related to the fractional quantum Hall effect.
- Q: How does this book relate to financial markets? A: The book discusses the relevance of path integrals to financial markets, specifically improvements to the Black-Scholes formula for option pricing, addressing the occurrence of large fluctuations in market behavior.