Path Integral Methods in Quantum Statistics, Quantum Field Theory and Membrane Physics PDF Download
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Author: Michael Bachmann
Publisher:
ISBN:
Category :
Languages : en
Pages : 209
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Author: Michael Bachmann
Publisher:
ISBN:
Category :
Languages : en
Pages : 209
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Book Description
Author: M Chaichian
Publisher: CRC Press
ISBN: 1482268914
Category : Science
Languages : en
Pages : 359
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Book Description
The path integral approach has proved extremely useful for the understanding of the most complex problems in quantum field theory, cosmology, and condensed matter physics. Path Integrals in Physics: Volume II, Quantum Field Theory, Statistical Physics and other Modern Applications covers the fundamentals of path integrals, both the Wiener and Feynman types, and their many applications in physics. The book deals with systems that have an infinite number of degrees of freedom. It discusses the general physical background and concepts of the path integral approach used, followed by a detailed presentation of the most typical and important applications as well as problems with either their solutions or hints how to solve them. Each chapter is self-contained and can be considered as an independent textbook. It provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers.
Author: George J. Papadopoulos
Publisher: Springer Science & Business Media
ISBN: 1468491407
Category : Science
Languages : en
Pages : 516
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Book Description
The Advanced Study Institute on "Path Integrals and Their Applications in Quantum, Statistical, and Solid State Physics" was held at the University of Antwerpen (R.U.C.A.), July 17-30, 1977. The Institute was sponsored by NATO. Co-sponsors were: A.C.E.C. (Belgium), Agfa-Gevaert (Belgium), l'Air Li~uide BeIge (Belgium), Be1gonucleaire (Belgium), Bell Telephone Mfg. Co. (Belgium), Boelwerf (Belgium), Generale BankmaatschappiJ (Belgium), I.B.M. (Belgium), Kredietbank (Belgium), National Science Foundation (U.S.A.), Siemens (Belgium). A total of 100 lecturers and partici pants attended the Institute. The development of path (or functional) integrals in relation to problems of stochastic nature dates back to the early 20's. At that time, Wiener succeeded in obtaining the fundamental solution of the diffusion e~uation using Einstein's joint probability of finding a Brownian particle in a succession of space intervals during a corresponding succession of time intervals. Dirac in the early 30's sowed the seeds of the path integral formulation of ~uantum mecha nics. However, the major and decisive step in this direction was taken with Feynman's works in ~uantum and statistical physics, and quantum electrodynamicso The applications now extend to areas such as continuous mechanics, and recently functional integration methods have been employed by Edwards for the study of polymerized matter
Author: Hagen Kleinert
Publisher: World Scientific
ISBN: 9789812381071
Category : Science
Languages : en
Pages : 1512
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Book Description
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.
Author: Gert Roepstorff
Publisher: Springer Science & Business Media
ISBN: 3642578861
Category : Science
Languages : en
Pages : 400
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Book Description
Specifically designed to introduce graduate students to the functional integration method in contemporary physics as painlessly as possible, the book concentrates on the conceptual problems inherent in the path integral formalism. Throughout, the striking interplay between stochastic processes, statistical physics and quantum mechanics comes to the fore, and all the methods of fundamental interest are generously illustrated by important physical examples.
Author: Mark S. Swanson
Publisher: Courier Corporation
ISBN: 0486493067
Category : Science
Languages : en
Pages : 463
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Book Description
Graduate-level, systematic presentation of path integral approach to calculating transition elements, partition functions, and source functionals. Covers Grassmann variables, field and gauge field theory, perturbation theory, and nonperturbative results. 1992 edition.
Author: Frederik W. Wiegel
Publisher: World Scientific
ISBN: 9789971978709
Category : Science
Languages : en
Pages : 226
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Book Description
This monograph distills material prepared by the author for class lectures, conferences and research seminars. It fills in a much-felt gap between the older and original work by Feynman and Hibbs and the more recent and advanced volume by Schulman. After presenting an elementary account on the Wiener path integral as applied to Brownian motion, the author progresses on to the statistics of polymers and polymer entanglements. The next three chapters provide an introduction to quantum statistical physics with emphasis on the conceptual understanding of many-variable systems. A chapter on the renormalization group provides material for starting on research work. The final chapter contains an over view of the role of path integrals in recent developments in physics. A good bibliography is provided for each chapter.
Author: Hagen Kleinert
Publisher: World Scientific
ISBN: 9814365262
Category : Science
Languages : en
Pages : 1626
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Book Description
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 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 time-sliced formula to include singular attractive 1/r- and 1/r2-potentials. The second is a new nonholonomic mapping principle carrying physical laws in flat spacetime to spacetimes 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, coordinate-independent 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 Feynman-Kleinert 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 strong-coupling 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 large-order behavior of perturbation expansions. A variational treatment extends the range of validity to small barriers. A corresponding extension of the large-order 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 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, recently experienced in the world markets, that large fluctuations occur much more frequently than in Gaussian distributions.
Author: Ulrich Mosel
Publisher: Springer Science & Business Media
ISBN: 9783540403821
Category : Mathematics
Languages : en
Pages : 232
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Book Description
Concise textbook intended as a primer on path integral formalism both in classical and quantum field theories, although emphasis is on the latter. It is ideally suited as an intensive one-semester course, delivering the basics needed by readers to follow developments in field theory. Path Integrals in Field Theory paves the way for both more rigorous studies in fundamental mathematical issues as well as for applications in hadron, particle and nuclear physics, thus addressing students in mathematical and theoretical physics alike. Assuming some background in relativistic quantum theory (but none in field theory), it complements the authors monograph Fields, Symmetries, and Quarks (Springer, 1999).
Author: Hagen Kleinert
Publisher: World Scientific Publishing Company Incorporated
ISBN: 9789810201975
Category : Science
Languages : en
Pages : 664
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Book Description
