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Author: Mikio Namiki
Publisher: Springer Science & Business Media
ISBN: 3540472177
Category : Science
Languages : en
Pages : 227
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Book Description
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: Mikio Namiki
Publisher: Springer Science & Business Media
ISBN: 3540472177
Category : Science
Languages : en
Pages : 227
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Book Description
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: P Damgaard
Publisher: World Scientific
ISBN: 9814578959
Category : Science
Languages : en
Pages : 508
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Book Description
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: Mikio Namiki
Publisher:
ISBN: 9783662138793
Category :
Languages : en
Pages : 228
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Book Description
Author: G. Menezes
Publisher:
ISBN:
Category : Scalar field theory
Languages : en
Pages : 32
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Book Description
Author: Michio Masujima
Publisher: Springer Science & Business Media
ISBN: 3540878513
Category : Science
Languages : en
Pages : 286
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Book Description
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: P. Bandyopadhyay
Publisher: Springer Science & Business Media
ISBN: 9401154260
Category : Science
Languages : en
Pages : 236
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Book Description
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: G. Menezes
Publisher:
ISBN:
Category : Langevin equations
Languages : en
Pages : 22
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Book Description
Author: G. Menezes
Publisher:
ISBN:
Category : Langevin equation
Languages : en
Pages : 20
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Book Description
Author: René Carmona
Publisher: American Mathematical Soc.
ISBN: 0821821008
Category : Stochastic partial differential equations
Languages : en
Pages : 349
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Book Description
The field of Stochastic Partial Differential Equations (SPDEs) is one of the most dynamically developing areas of mathematics. It lies at the cross section of probability, partial differential equations, population biology, and mathematical physics. The field is especially attractive because of its interdisciplinary nature and the enormous richness of current and potential future applications. This volume is a collection of six important topics in SPDEs presented from the viewpoint of distinguished scientists working in the field and related areas. Emphasized are the genesis and applications of SPDEs as well as mathematical theory and numerical methods. .
Author: S. Chaturvedi
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 216
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Book Description
