Path Integral Quantization And Stochastic Quantization

Author : Michio Masujima
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 50,5 Mb
Release : 2008-11-21
Category : Science
ISBN : 9783540878513

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Path Integral Quantization and Stochastic Quantization by Michio Masujima Pdf

In this book, we discuss the path integral quantization and the stochastic quantization of classical mechanics and classical field theory. Forthe description ofthe classical theory, we have two methods, one based on the Lagrangian formalism and the other based on the Hamiltonian formal ism. The Hamiltonian formalism is derived from the Lagrangian·formalism. In the standard formalism ofquantum mechanics, we usually make use ofthe Hamiltonian formalism. This fact originates from the following circumstance which dates back to the birth of quantum mechanics. The first formalism ofquantum mechanics is Schrodinger's wave mechan ics. In this approach, we regard the Hamilton-Jacobi equation of analytical mechanics as the Eikonal equation of "geometrical mechanics". Based on the optical analogy, we obtain the Schrodinger equation as a result ofthe inverse of the Eikonal approximation to the Hamilton-Jacobi equation, and thus we arrive at "wave mechanics". The second formalism ofquantum mechanics is Heisenberg's "matrix me chanics". In this approach, we arrive at the Heisenberg equation of motion from consideration of the consistency of the Ritz combination principle, the Bohr quantization condition and the Fourier analysis of a physical quantity. These two formalisms make up the Hamiltonian.formalism of quantum me chanics.

Author : Mikio Namiki
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 44,7 Mb
Release : 2008-10-04
Category : Science
ISBN : 9783540472179

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Stochastic Quantization by Mikio Namiki Pdf

This is a textbook on stochastic quantization which was originally proposed by G. Parisi and Y. S. Wu in 1981 and then developed by many workers. I assume that the reader has finished a standard course in quantum field theory. The Parisi-Wu stochastic quantization method gives quantum mechanics as the thermal-equilibrium limit of a hypothetical stochastic process with respect to some fictitious time other than ordinary time. We can consider this to be a third method of quantization; remarkably different from the conventional theories, i. e, the canonical and path-integral ones. Over the past ten years, we have seen the technical merits of this method in quantizing gauge fields and in performing large numerical simulations, which have never been obtained by the other methods. I believe that the stochastic quantization method has the potential to extend the territory of quantum mechanics and of quantum field theory. However, I should remark that stochastic quantization is still under development through many mathematical improvements and physical applications, and also that the fictitious time of the theory is only a mathematical tool, for which we do not yet know its origin in the physical background. For these reasons, in this book, I attempt to describe its theoretical formulation in detail as well as practical achievements.

Author : SWANSON
Publisher : IOP Publishing Limited
Page : 241 pages
File Size : 51,6 Mb
Release : 2020-08-06
Category : Mathematical physics
ISBN : 0750335459

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Path Integral Quantization Hb by SWANSON Pdf

This book is a self-contained and concise introduction to the techniques and applications of path integral quantization and functional techniques, aimed at students and practitioners. The first half of the text focuses on quantum mechanics, including a review of the action formulation of classical mechanics and quantum mechanics in the Dirac operator and state formalism, and further examination of the path integral. The second part examines relativistic field theories, reviewing special relativity, as well as derivation of the path integral representation of the vacuum transition element for quantized scalar, spinor, and vector fields from the coherent state representation of the respective field theories. Key Features Concise introduction to the derivation and methods of path integral approaches to quantum mechanics and quantum field theory. Self-contained guide for students and practitioners

Author : Mikio Namiki
Publisher : Unknown
Page : 228 pages
File Size : 40,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662138794

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Stochastic Quantization by Mikio Namiki Pdf

Author : M Chaichian,A Demichev
Publisher : CRC Press
Page : 359 pages
File Size : 45,7 Mb
Release : 2018-10-08
Category : Science
ISBN : 9781482268911

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Path Integrals in Physics by M Chaichian,A Demichev Pdf

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 : Mark S Swanson
Publisher : Unknown
Page : 242 pages
File Size : 53,6 Mb
Release : 2020-08-07
Category : Electronic
ISBN : 0750335483

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Path Integral Quantization by Mark S Swanson Pdf

This book is a self-contained and concise introduction to the techniques and applications of path integral quantization and functional techniques, aimed at students and practitioners. The first half of the text focuses on quantum mechanics, including a review of the action formulation of classical mechanics and quantum mechanics in the Dirac operator and state formalism, and further examination of the path integral. The second part examines relativistic field theories, reviewing special relativity, as well as derivation of the path integral representation of the vacuum transition element for quantized scalar, spinor, and vector fields from the coherent state representation of the respective field theories. Key Features Concise introduction to the derivation and methods of path integral approaches to quantum mechanics and quantum field theory. Self-contained guide for students and practitioners

Author : M Chaichian,A Demichev
Publisher : CRC Press
Page : 360 pages
File Size : 46,8 Mb
Release : 2001-07-01
Category : Science
ISBN : 075030801X

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Path Integrals in Physics by M Chaichian,A Demichev Pdf

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.

Author : Poul Henrik Damgaard,Helmuth Hffel
Publisher : World Scientific
Page : 512 pages
File Size : 47,6 Mb
Release : 1988
Category : Science
ISBN : 9971502542

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Stochastic Quantization by Poul Henrik Damgaard,Helmuth Hffel Pdf

This collection of selected reprints presents as broad a selection as possible, emphasizing formal and numerical aspects of Stochastic Quantization. It reviews and explains the most important concepts placing selected reprints and crucial papers into perspective and compact form.

Author : P. Bandyopadhyay
Publisher : Springer Science & Business Media
Page : 236 pages
File Size : 51,6 Mb
Release : 2013-03-07
Category : Science
ISBN : 9789401154260

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Geometry, Topology and Quantization by P. Bandyopadhyay Pdf

This is a monograph on geometrical and topological features which arise in various quantization procedures. Quantization schemes consider the feasibility of arriving at a quantum system from a classical one and these involve three major procedures viz. i) geometric quantization, ii) Klauder quantization, and iii) stochastic quanti zation. In geometric quantization we have to incorporate a hermitian line bundle to effectively generate the quantum Hamiltonian operator from a classical Hamil tonian. Klauder quantization also takes into account the role of the connection one-form along with coordinate independence. In stochastic quantization as pro posed by Nelson, Schrodinger equation is derived from Brownian motion processes; however, we have difficulty in its relativistic generalization. It has been pointed out by several authors that this may be circumvented by formulating a new geometry where Brownian motion proceses are considered in external as well as in internal space and, when the complexified space-time is considered, the usual path integral formulation is achieved. When this internal space variable is considered as a direc tion vector introducing an anisotropy in the internal space, we have the quantization of a Fermi field. This helps us to formulate a stochastic phase space formalism when the internal extension can be treated as a gauge theoretic extension. This suggests that massive fermions may be considered as Skyrme solitons. The nonrelativistic quantum mechanics is achieved in the sharp point limit.

Author : Brian Hatfield
Publisher : CRC Press
Page : 756 pages
File Size : 48,5 Mb
Release : 2018-03-09
Category : Science
ISBN : 9780429972867

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Quantum Field Theory Of Point Particles And Strings by Brian Hatfield Pdf

First Published in 2018. Routledge is an imprint of Taylor & Francis, an Informa company.

Author : Heimo Latal,Wolfgang Schweiger
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 46,9 Mb
Release : 2001-07-17
Category : Science
ISBN : 9783540421009

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Methods of Quantization by Heimo Latal,Wolfgang Schweiger Pdf

Author : P Damgaard,H Hüffel
Publisher : World Scientific
Page : 508 pages
File Size : 45,5 Mb
Release : 1988-02-01
Category : Science
ISBN : 9789814578950

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Stochastic Quantization by P Damgaard,H Hüffel Pdf

This collection of selected reprints presents as broad a selection as possible, emphasizing formal and numerical aspects of Stochastic Quantization. It reviews and explains the most important concepts placing selected reprints and crucial papers into perspective and compact form. Contents: The Classic (G Parisi & Y-S Wu)Perturbation Theory (E Floratos et al.)Gauge Fields (D Zwanziger et al.)Fermions (P Damgaard et al.)Gravity (H Rumpf)Supersymmetry (G Parisi et al.)Canonical Stochastic Quantization (S Ryang et al.)Stochastic Regularization (J Briet et al.)A Rigorous Construction (G Jona-Lasinio & P Mitter)Large-N Limit (J Greensite et al.)Complex Actions (G Parisi et al.)Minkowski Space (H Hüffel et al.)Numerical Applications (G Parisi et al.)and other papers Readership: Physicists and mathematical physicists.

Author : Dmitri Gitman,Igor V. Tyutin
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642839382

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Quantization of Fields with Constraints by Dmitri Gitman,Igor V. Tyutin Pdf

Gauge field theories underlie all models now used in elementary particle physics. These theories refer to the class of singular theories which are also theories with constraints. The quantization of singular theories remains one of the key problems of quantum field theory and is being intensively discussed in the literature. This book is an attempt to fill the need for a comprehensive analysis of this problem, which has not heretofore been met by the available monographs and reviews. The main topics are canonical quantization and the path integral method. In addition, the Lagrangian BRST quantization is completely described, for the first time in a monograph. The book also presents a number of original results obtained by the authors, in particular, a complete description of the physical sector of an arbitrary gauge theory, quantization of singular theories with higher theories with time-dependent constraints, and correct derivatives, quantization of canonical quantization of theories of a relativistic point-like particle. As a general illustration we present quantization of field theories such as electrodynamics, Yang-Mills theory, and gravity. It should be noted that this monograph is aimed not only at giving the reader the rules of quantization according to the principle "if you do it this way, it will be good", but also at presenting strong arguments based on the modem interpretation of the classical and quantum theories which show that these methods· are the natural, if not the only possible ones.

Author : Mark S. Swanson
Publisher : Courier Corporation
Page : 464 pages
File Size : 42,9 Mb
Release : 2014-02-19
Category : Science
ISBN : 9780486782300

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Path Integrals and Quantum Processes by Mark S. Swanson Pdf

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 : B. Sakita
Publisher : World Scientific Publishing Company
Page : 234 pages
File Size : 49,6 Mb
Release : 1985
Category : Mathematics
ISBN : 9971978555

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Quantum Theory of Many-variable Systems and Fields by B. Sakita Pdf

These lecture notes are based on special courses on Field Theory and Statistical Mechanics given for graduate students at the City College of New York. It is an ideal text for a one-semester course on Quantum Field Theory.