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Quantum Mechanics And Path Integrals

Autor: Richard P. Feynman
Publisher: Courier Corporation
ISBN: 0486477223
File Size: 12,37 MB
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Looks at quantum mechanics, covering such topics as perturbation method, statistical mechanics, path integrals, and quantum electrodynamics.

Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets

Autor: Hagen Kleinert
Publisher: World Scientific
ISBN: 9814273570
File Size: 5,87 MB
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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." "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 that large market fluctuations occur much more frequently than in Gaussian distributions." --Book Jacket.

Path Integrals In Quantum Mechanics

Autor: Jean Zinn-Justin
Publisher: Oxford University Press
ISBN: 0198566751
File Size: 7,93 MB
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Quantum field theory is hardly comprehensible without path integrals: the goal of this book is to introduce students to this topic within the context of ordinary quantum mechanics and non-relativistic many-body theory, before facing the problems associated with the more involved quantum field theory formalism.

Path Integrals And Quantum Processes

Autor: Mark S. Swanson
Publisher: Courier Corporation
ISBN: 0486493067
File Size: 7,68 MB
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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.

Path Integrals In Physics

Autor: M Chaichian
Publisher: CRC Press
ISBN: 9780750308014
File Size: 6,90 MB
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Path Integrals in Physics: Volume I, Stochastic Processes and Quantum Mechanics presents the fundamentals of path integrals, both the Wiener and Feynman type, and their many applications in physics. Accessible to a broad community of theoretical physicists, the book deals with systems possessing a infinite number of degrees in 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. It describes in detail various applications, including systems with Grassmann variables. Each chapter is self-contained and can be considered as an independent textbook. The book provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers.

Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets

Autor: Hagen Kleinert
Publisher: World Scientific Publishing Company Incorporated
ISBN:
File Size: 23,58 MB
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This is the fourth, 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 perturbation expansions. A newvariational 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 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 given which account for the fact that large market fluctuations occur much more frequently than in the commonly used Gaussian distributions. The author's other book on 'Critical Properties of φ 4 Theories' gives a thorough introduction to the field of critical phenomena and develops new powerful resummation techniques for the extraction of physical results from the divergent perturbation expansions.

Introduction To Quantum Mechanics

Autor: H. J. W. Mller-Kirsten
Publisher: World Scientific
ISBN: 9812566910
File Size: 22,98 MB
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After a consideration of basic quantum mechanics, this introduction aims at a side by side treatment of fundamental applications of the Schr”dinger equation on the one hand and the applications of the path integral on the other. Different from traditional texts and using a systematic perturbation method, the solution of Schr”dinger equations includes also those with anharmonic oscillator potentials, periodic potentials, screened Coulomb potentials and a typical singular potential, as well as the investigation of the large order behavior of the perturbation series. On the path integral side, after introduction of the basic ideas, the expansion around classical configurations in Euclidean time, such as instantons, is considered, and the method is applied in particular to anharmonic oscillator and periodic potentials. Numerous other aspects are treated on the way, thus providing the reader an instructive overview over diverse quantum mechanical phenomena, e.g. many other potentials, Green's functions, comparison with WKB, calculation of lifetimes and sojourn times, derivation of generating functions, the Coulomb problem in various coordinates, etc. All calculations are given in detail, so that the reader can follow every step.

Introduction To Quantum Mechanics

Autor: Harald J W Müller-Kirsten
Publisher: World Scientific Publishing Company
ISBN: 9814397768
File Size: 24,54 MB
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This text on quantum mechanics begins by covering all the main topics of an introduction to the subject. It then concentrates on newer developments. In particular it continues with the perturbative solution of the Schrödinger equation for various potentials and thereafter with the introduction and evaluation of their path integral counterparts. Considerations of the large order behavior of the perturbation expansions show that in most applications these are asymptotic expansions. The parallel consideration of path integrals requires the evaluation of these around periodic classical configurations, the fluctuation equations about which lead back to specific wave equations. The period of the classical configurations is related to temperature, and permits transitions to the thermal domain to be classified as phase transitions. In this second edition of the text important applications and numerous examples have been added. In particular, the chapter on the Coulomb potential has been extended to include an introduction to chemical bonds, the chapter on periodic potentials has been supplemented by a section on the band theory of metals and semiconductors, and in the chapter on large order behavior a section has been added illustrating the success of converging factors in the evaluation of asymptotic expansions. Detailed calculations permit the reader to follow every step.

Field Theory

Autor: Ashok Das
Publisher: World Scientific
ISBN: 9789810213978
File Size: 5,51 MB
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Traditionally, field theory is taught through canonical quantization with a heavy emphasis on high energy physics. However, the techniques of field theory are applicable as well and are extensively used in various other areas of physics such as consdensed matter, nuclear physics and statistical mechanics. The path integral approach brings out this feature most clearly. In this book, the path integral approach is developed in detail completely within the context of quantum mechanics. Subsequently, it is applied to various areas of physics.