C Algebras And Mathematical Foundations Of Quantum Statistical Mechanics
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Author |
: Jean-Bernard Bru |
Publisher |
: Springer Nature |
Total Pages |
: 497 |
Release |
: 2023-06-16 |
ISBN-10 |
: 9783031289491 |
ISBN-13 |
: 3031289498 |
Rating |
: 4/5 (91 Downloads) |
Synopsis C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics by : Jean-Bernard Bru
This textbook provides a comprehensive introduction to the mathematical foundations of quantum statistical physics. It presents a conceptually profound yet technically accessible path to the C*-algebraic approach to quantum statistical mechanics, demonstrating how key aspects of thermodynamic equilibrium can be derived as simple corollaries of classical results in convex analysis. Using C*-algebras as examples of ordered vector spaces, this book makes various aspects of C*-algebras and their applications to the mathematical foundations of quantum theory much clearer from both mathematical and physical perspectives. It begins with the simple case of Gibbs states on matrix algebras and gradually progresses to a more general setting that considers the thermodynamic equilibrium of infinitely extended quantum systems. The book also illustrates how first-order phase transitions and spontaneous symmetry breaking can occur, in contrast to the finite-dimensional situation. One of the unique features of this book is its thorough and clear treatment of the theory of equilibrium states of quantum mean-field models. This work is self-contained and requires only a modest background in analysis, topology, and functional analysis from the reader. It is suitable for both mathematicians and physicists with a specific interest in quantum statistical physics.
Author |
: Klaas Landsman |
Publisher |
: |
Total Pages |
: 880 |
Release |
: 2020-10-09 |
ISBN-10 |
: 1013278364 |
ISBN-13 |
: 9781013278365 |
Rating |
: 4/5 (64 Downloads) |
Synopsis Foundations of Quantum Theory by : Klaas Landsman
This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Author |
: A.R. Marlow |
Publisher |
: Elsevier |
Total Pages |
: 383 |
Release |
: 2012-12-02 |
ISBN-10 |
: 9780323141185 |
ISBN-13 |
: 0323141188 |
Rating |
: 4/5 (85 Downloads) |
Synopsis Mathematical Foundations of Quantum Theory by : A.R. Marlow
Mathematical Foundations of Quantum Theory is a collection of papers presented at the 1977 conference on the Mathematical Foundations of Quantum Theory, held in New Orleans. The contributors present their topics from a wide variety of backgrounds and specialization, but all shared a common interest in answering quantum issues. Organized into 20 chapters, this book's opening chapters establish a sound mathematical basis for quantum theory and a mode of observation in the double slit experiment. This book then describes the Lorentz particle system and other mathematical structures with which fundamental quantum theory must deal, and then some unsolved problems in the quantum logic approach to the foundations of quantum mechanics are considered. Considerable chapters cover topics on manuals and logics for quantum mechanics. This book also examines the problems in quantum logic, and then presents examples of their interpretation and relevance to nonclassical logic and statistics. The accommodation of conventional Fermi-Dirac and Bose-Einstein statistics in quantum mechanics or quantum field theory is illustrated. The final chapters of the book present a system of axioms for nonrelativistic quantum mechanics, with particular emphasis on the role of density operators as states. Specific connections of this theory with other formulations of quantum theory are also considered. These chapters also deal with the determination of the state of an elementary quantum mechanical system by the associated position and momentum distribution. This book is of value to physicists, mathematicians, and researchers who are interested in quantum theory.
Author |
: Michael Spivak |
Publisher |
: |
Total Pages |
: 733 |
Release |
: 2010 |
ISBN-10 |
: 0914098322 |
ISBN-13 |
: 9780914098324 |
Rating |
: 4/5 (22 Downloads) |
Synopsis Physics for Mathematicians by : Michael Spivak
Author |
: F. Strocchi |
Publisher |
: World Scientific |
Total Pages |
: 193 |
Release |
: 2008 |
ISBN-10 |
: 9789812835222 |
ISBN-13 |
: 9812835229 |
Rating |
: 4/5 (22 Downloads) |
Synopsis An Introduction to the Mathematical Structure of Quantum Mechanics by : F. Strocchi
Arising out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students, this book formulates the mathematical structure of QM in terms of the C*-algebra of observables, which is argued on the basis of the operational definition of measurements and the duality between states and observables.
Author |
: L. D. Faddeev |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 250 |
Release |
: 2009 |
ISBN-10 |
: 9780821846995 |
ISBN-13 |
: 082184699X |
Rating |
: 4/5 (95 Downloads) |
Synopsis Lectures on Quantum Mechanics for Mathematics Students by : L. D. Faddeev
Describes the relation between classical and quantum mechanics. This book contains a discussion of problems related to group representation theory and to scattering theory. It intends to give a mathematically oriented student the opportunity to grasp the main points of quantum theory in a mathematical framework.
Author |
: Leon Armenovich Takhtadzhi͡an |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 410 |
Release |
: 2008 |
ISBN-10 |
: 9780821846308 |
ISBN-13 |
: 0821846302 |
Rating |
: 4/5 (08 Downloads) |
Synopsis Quantum Mechanics for Mathematicians by : Leon Armenovich Takhtadzhi͡an
Presents a comprehensive treatment of quantum mechanics from a mathematics perspective. Including traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin.
Author |
: John von Neumann |
Publisher |
: Princeton University Press |
Total Pages |
: 462 |
Release |
: 1955 |
ISBN-10 |
: 0691028931 |
ISBN-13 |
: 9780691028934 |
Rating |
: 4/5 (31 Downloads) |
Synopsis Mathematical Foundations of Quantum Mechanics by : John von Neumann
A revolutionary book that for the first time provided a rigorous mathematical framework for quantum mechanics. -- Google books
Author |
: Ola Bratteli |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 510 |
Release |
: 2013-03-14 |
ISBN-10 |
: 9783662025208 |
ISBN-13 |
: 3662025205 |
Rating |
: 4/5 (08 Downloads) |
Synopsis Operator Algebras and Quantum Statistical Mechanics 1 by : Ola Bratteli
In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of develop ment it was realized that this would entail the omission ofvarious interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems of field theory and statistical mechanics. But the theory of 20 years aga was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honey moon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e. g. asymptotic abelian ness and KMS states, new techniques applied, e. g. the Choquet theory of barycentric decomposition for states, and new structural results obtained, e. g. the existence of a continuum of nonisomorphic type-three factors.
Author |
: Frederick W. Byron |
Publisher |
: Courier Corporation |
Total Pages |
: 674 |
Release |
: 2012-04-26 |
ISBN-10 |
: 9780486135069 |
ISBN-13 |
: 0486135063 |
Rating |
: 4/5 (69 Downloads) |
Synopsis Mathematics of Classical and Quantum Physics by : Frederick W. Byron
Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.