Author : Luigi Accardi
Publisher : Springer Science & Business Media
Page : 485 pages
File Size : 32,82 MB
Release : 2013-03-14
Category : Science
ISBN : 3662049295
Well suited as a textbook in the emerging field of stochastic limit, which is a new mathematical technique developed for solving nonlinear problems in quantum theory.
Author : Eduard Prugovečki
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 34,95 MB
Release : 1984-01-31
Category : Gardening
ISBN : 9789027716170
The principal intent of this monograph is to present in a systematic and self-con tained fashion the basic tenets, ideas and results of a framework for the consistent unification of relativity and quantum theory based on a quantum concept of spacetime, and incorporating the basic principles of the theory of stochastic spaces in combination with those of Born's reciprocity theory. In this context, by the physicial consistency of the present framework we mean that the advocated approach to relativistic quantum theory relies on a consistent probabilistic interpretation, which is proven to be a direct extrapolation of the conventional interpretation of nonrelativistic quantum mechanics. The central issue here is that we can derive conserved and relativistically convariant probability currents, which are shown to merge into their nonrelativistic counterparts in the nonrelativistic limit, and which at the same time explain the physical and mathe matical reasons behind the basic fact that no probability currents that consistently describe pointlike particle localizability exist in conventional relativistic quantum mechanics. Thus, it is not that we dispense with the concept oflocality, but rather the advanced central thesis is that the classical concept of locality based on point like localizability is inconsistent in the realm of relativistic quantum theory, and should be replaced by a concept of quantum locality based on stochastically formulated systems of covariance and related to the aforementioned currents.
Author : L. Accardi
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 22,58 MB
Release : 1998-03-27
Category : Gardening
ISBN : 9780387984582
Senior probabilists from around the world with widely differing specialities gave their visions of the state of their specialty, why they think it is important, and how they think it will develop in the new millenium. The volume includes papers given at a symposium at Columbia University in 1995, but papers from others not at the meeting were added to broaden the coverage of areas. All papers were refereed.
Author : Mikio Namiki
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 20,93 MB
Release : 2008-10-04
Category : Science
ISBN : 3540472177
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 : A. O. Bolivar
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 20,20 MB
Release : 2004-01-22
Category : Mathematics
ISBN : 9783540201465
At what level of physical existence does "quantum behavior" begin? How does it develop from classical mechanics? This book addresses these questions and thereby sheds light on fundamental conceptual problems of quantum mechanics. It elucidates the problem of quantum-classical correspondence by developing a procedure for quantizing stochastic systems (e.g. Brownian systems) described by Fokker-Planck equations. The logical consistency of the scheme is then verified by taking the classical limit of the equations of motion and corresponding physical quantities. Perhaps equally important, conceptual problems concerning the relationship between classical and quantum physics are identified and discussed. Graduate students and physical scientists will find this an accessible entrée to an intriguing and thorny issue at the core of modern physics.
Author : Noboru Watanabe
Publisher : World Scientific
Page : 489 pages
File Size : 46,17 MB
Release : 2008-02-19
Category : Science
ISBN : 9814471550
This volume is a collection of articles written by Professor M Ohya over the past three decades in the areas of quantum teleportation, quantum information theory, quantum computer, etc. By compiling Ohya's important works in these areas, the book serves as a useful reference for researchers who are working in these fields.
Author : Robert B. Griffiths
Publisher : Cambridge University Press
Page : 412 pages
File Size : 28,38 MB
Release : 2003-11-13
Category : Science
ISBN : 9780521539296
Quantum mechanics is one of the most fundamental yet difficult subjects in physics. Nonrelativistic quantum theory is presented here in a clear and systematic fashion, integrating Born's probabilistic interpretation with Schrödinger dynamics. Basic quantum principles are illustrated with simple examples requiring no mathematics beyond linear algebra and elementary probability theory. The quantum measurement process is consistently analyzed using fundamental quantum principles without referring to measurement. These same principles are used to resolve several of the paradoxes that have long perplexed physicists, including the double slit and Schrödinger's cat. The consistent histories formalism used here was first introduced by the author, and extended by M. Gell-Mann, J. Hartle and R. Omnès. Essential for researchers yet accessible to advanced undergraduate students in physics, chemistry, mathematics, and computer science, this book is supplementary to standard textbooks. It will also be of interest to physicists and philosophers working on the foundations of quantum mechanics.
Author : Sergio Albeverio
Publisher : World Scientific
Page : 466 pages
File Size : 12,75 MB
Release : 2000
Category : Science
ISBN : 9789810244408
In October 1998 a conference was held in Lisbon to celebrate Ludwig Streit's 60th birthday. This book collects some of the papers presented at the conference as well as other essays contributed by the many friends and collaborators who wanted to honor Ludwig Streit's scientific career and personality.The contributions cover many aspects of contemporary mathematical physics. Of particular importance are new results on infinite-dimensional stochastic analysis and its applications to a wide range of physical domains.List of Contributors: S Albeverio, T Hida, L Accardi, I Ya Aref'eva, I V Volovich; A Daletskii, Y Kondratiev, W Karwowski, N Asai, I Kubo, H-H Kuo, J Beckers, Ph Blanchard, G F Dell'Antonio, D Gandolfo, M Sirugue-Collin, A Bohm, H Kaldass, D Boll, G Jongen, G M Shim, J Bornales, C C Bernido, M V Carpio-Bernido, G Burdet, Ph Combe, H Nencka, P Cartier, C DeWitt-Morette, H Ezawa, K Nakamura, K Watanabe, Y Yamanaka, R Figari, F Gesztesy, H Holden, R Gielerak, G A Goldin, Z Haba, M-O Hongler, Y Hu, B Oksendal, A Sulem, J R Klauder, C B Lang, V I Man'ko, H Ouerdiane, J Potthoff, E Smajlovic, M Rckner, E Scacciatelli, J L Silva, J Stochel, F H Szafraniec, L V zquez, D N Kozakevich, S Jimnez, V R Vieira, P D Sacramento, R Vilela Mendes, D Voln?, P Samek.
Author : John C Baez
Publisher : World Scientific
Page : 276 pages
File Size : 44,26 MB
Release : 2018-02-14
Category : Science
ISBN : 981322696X
We introduce the theory of chemical reaction networks and their relation to stochastic Petri nets — important ways of modeling population biology and many other fields. We explain how techniques from quantum mechanics can be used to study these models. This relies on a profound and still mysterious analogy between quantum theory and probability theory, which we explore in detail. We also give a tour of key results concerning chemical reaction networks and Petri nets.
Author : Noboru Watanabe
Publisher : World Scientific
Page : 306 pages
File Size : 49,48 MB
Release : 2023-10-25
Category : Mathematics
ISBN : 9811276005
This volume aims to return to the starting point of the fields of infinite dimensional analysis and quantum probability, fields that are growing rapidly at present, and to seriously attempt mutual interaction between the two, with a view to enumerating and solving the many fundamental problems they entail. For such a purpose, we look for interdisciplinary bridges in mathematics including classical probability and to different branches of physics, in particular, research for new paradigms for information science on the basis of quantum theory.
