Stochastic Quantization
Stochastic Quantization

Author: Mikio Namiki

Publisher: Springer Science & Business Media

Published: 2008-10-04

Total Pages: 227

ISBN-13: 3540472177

DOWNLOAD EBOOK

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
Stochastic Quantization

Author: Poul Henrik Damgaard

Publisher: World Scientific

Published: 1988

Total Pages: 512

ISBN-13: 9789971502546

DOWNLOAD EBOOK

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.

Quarks, Symmetries And Strings - A Symposium In Honor Of Bunji Sakita's 60th Birthday
Quarks, Symmetries And Strings - A Symposium In Honor Of Bunji Sakita's 60th Birthday

Author: Michio Kaku

Publisher: World Scientific

Published: 1991-04-30

Total Pages: 436

ISBN-13: 9814569283

DOWNLOAD EBOOK

Quarks, Symmetries and Strings is a book that reflects the rich diversity of current research in physics: it describes quantum chromodynamics, quark phenomenology, superstring theory, supersymmetry, matrix models, statistical methods, superconductivity and neural networks. The book also reflects the diversity of Dr Bunji Sakita's scientific work. Dr Sakita has made seminal contributions in many of these areas. The book celebrates the many path-breaking ideas he pioneered which still cross-fertilize many of the most active areas of current research.

Path Integral Quantization and Stochastic Quantization
Path Integral Quantization and Stochastic Quantization

Author: Michio Masujima

Publisher: Springer Science & Business Media

Published: 2008-11-21

Total Pages: 286

ISBN-13: 3540878513

DOWNLOAD EBOOK

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.

Lattice Gauge Theory
Lattice Gauge Theory

Author: B. Bunk

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 328

ISBN-13: 1461322316

DOWNLOAD EBOOK

This volume presents the contributions to the international workshop entitled "Lattice Gauge Theory - a Challenge in Large Scale Computing" that was held in Wuppertal from November 4 to 7, 1985. This meeting was the third in a series of European workshops in this rapidly developing field. The meeting intended to bring together both active university research ers in this field and scientists from industry and research centers who pursue large scale computing projects on problems within lattice gauge theory. These problems are extremely demanding from the point of view of both machine hardware and algorithms, for the verification of the continuum fields theories like Quantum Chromodynamics in four-dimensional Euclidean space-time is quite cumbersome due to the tremendously large number of de grees of freedom. Yet the motivation of theoretical physicists to exploit computers as tools for the simulation of complex systems such as gauge field theories has grown considerably during the past years. In fact, quite a few prominent colleagues of ours have even gone into machine building, both in industry and research institutions: more parallelism, and more de dicated computer architecture are their design goals to help them boost the Megaflop rate in their simulation processes. The workshop contained several interesting seminars with status reports on such supercomputer projects like the Italian APE (by E. Marinari), the IBM project GF-11 (by D. Weingarten), and the Danish projects MOSES and PALLAS (by H. Bohr).

Spatio-temporal Chaos & Vacuum Fluctuations Of Quantized Fields
Spatio-temporal Chaos & Vacuum Fluctuations Of Quantized Fields

Author: Christian Beck

Publisher: World Scientific

Published: 2002-04-29

Total Pages: 292

ISBN-13: 9814489689

DOWNLOAD EBOOK

This book describes new applications for spatio-temporal chaotic dynamical systems in elementary particle physics and quantum field theories. The stochastic quantization approach of Parisi and Wu is extended to more general deterministic chaotic processes as generated by coupled map lattices. In particular, so-called chaotic strings are introduced as a suitable small-scale dynamics of vacuum fluctuations. This more general approach to second quantization reduces to the ordinary stochastic quantization scheme on large scales, but it also opens up interesting new perspectives: chaotic strings appear to minimize their vacuum energy for the observed numerical values of the free standard model parameters.