Stochastic Quantization
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Stochastic Quantization
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Author : Mikio Namiki
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-04
Stochastic Quantization written by Mikio Namiki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-04 with Science categories.
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.
Stochastic Quantization
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Author : Mikio Namiki
language : en
Publisher: Springer
Release Date : 2013-11-20
Stochastic Quantization written by Mikio Namiki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-20 with Science categories.
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.
Stochastic Quantization
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Author : Poul Henrik Damgaard
language : en
Publisher: World Scientific
Release Date : 1988
Stochastic Quantization written by Poul Henrik Damgaard and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Science categories.
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.
Path Integral Quantization And Stochastic Quantization
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Author : Michio Masujima
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-21
Path Integral Quantization And Stochastic Quantization written by Michio Masujima and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-21 with Science categories.
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.
Geometry Topology And Quantization
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Author : P. Bandyopadhyay
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-07
Geometry Topology And Quantization written by P. Bandyopadhyay and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Science categories.
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.
Path Integrals In Physics
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Author : M Chaichian
language : en
Publisher: CRC Press
Release Date : 2018-10-08
Path Integrals In Physics written by M Chaichian and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-08 with Science categories.
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.
Spatio Temporal Chaos And Vacuum Fluctuations Of Quantized Fields
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Author : Christian Beck
language : en
Publisher: World Scientific
Release Date : 2002
Spatio Temporal Chaos And Vacuum Fluctuations Of Quantized Fields written by Christian Beck and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Science categories.
"This book deals with new applications for coupled map lattices in quantum field theories and elementary particle physics"--P. xiii.
Fundamental Aspects Of Quantum Theory
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Author : Vittorio Gorini
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Fundamental Aspects Of Quantum Theory written by Vittorio Gorini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Thi's book collects the contributions to the NATO Advanced Research WJrkshop on "FundaIrental Aspects of Quantum 'Iheory," held at the Centro di Cultura Scientifica "Alessandro Volta," Villa Olma, Carro, Italy, 2-7 September 1985. The rreeting was dedicated to the rremory of the late pro fessor Piero Caldirola, a prominent member of the Physics Departrrent of the University of r1ilan and a native of Como. The aim of the workshop has been to present several recent experi rrental results and theoretical developrrents concerning the various fa cets of quantum physics. The breadth of scope of the rreeting was in accordance with Professor Caldirola's vast scientific interests, and fostered communication among experirrental physicists, theoretical and mathematical physicists, and nEthematicians, working in different but related fields. Indeed, lectu rers endeavoured to make their contributions understandable to people acquainted with the problem but not necessarily familiar with the tech nical details; and these efforts were successful, as indicated by the frequent private discussions which took place among participants belon ging to different breeds and brands. 1ne rreeting was made up of six one-day sessions, each of them addres sing to a specific aspect of quantum theory: 1. General Problems and Crucial Experinents; with emphasis on sin gle-particle interference eh rirrents of neutrons and of photons, and on the rreasurerrent problem. 2. Quantization and Stochastic Processes; including stochastic quan tization of gauge fields, stochastic description of supersyrnmetric fields, quantum stochastic calculus and stochastic mechanics."
Probabilistic Methods In Quantum Field Theory And Quantum Gravity
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Author : Poul Henrik Damgaard
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Probabilistic Methods In Quantum Field Theory And Quantum Gravity written by Poul Henrik Damgaard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
From August 21 through August 27, 1989 the Nato Advanced Research Workshop Probabilistic Methods in Quantum Field Theory and Quantum Gravity" was held at l'Institut d'Etudes Scientifiques, Cargese, France. This publication is the Proceedings of this workshop. The purpose of the workshop was to bring together a group of scientists who have been at the forefront of the development of probabilistic methods in Quantum Field Theory and Quantum Gravity. The original thought was to put emphasis on the introduction of stochastic processes in the understanding of Euclidean Quantum Field Theory, with also some discussion of recent progress in the field of stochastic numerical methods. During the final preparation of the meeting we broadened the scope to include all those Euclidean Quantum Field Theory descriptions that make direct reference to concepts from probability theory and statistical mechanics. Several of the main contributions centered around a more rigorous discussion of stochastic processes for the formulation of Euclidean Quantum Field Theory. These rather stringent mathematical approaches were contrasted with the more heuristic stochastic quantization scheme developed in 1981 by Parisi and Wu: Stochastic quan tization, its intrinsic BRST -structure and stochastic regularization appeared in many disguises and in connection with several different problems throughout the workshop.
Quantum Theory Of Many Variable Systems And Fields
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Author : B. Sakita
language : en
Publisher: World Scientific Publishing Company
Release Date : 1985
Quantum Theory Of Many Variable Systems And Fields written by B. Sakita and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
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.