C*-algebras and mathematical foundations of quantum statistical mechanics : an introduction / Jean-Bernard Bru, Walter Alberto de Siqueira Pedra.
2023
QC174.4
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Title
C*-algebras and mathematical foundations of quantum statistical mechanics : an introduction / Jean-Bernard Bru, Walter Alberto de Siqueira Pedra.
ISBN
9783031289491 (electronic bk.)
3031289498 (electronic bk.)
303128948X
9783031289484
3031289498 (electronic bk.)
303128948X
9783031289484
Published
Cham : Springer, [2023]
Copyright
©2023
Language
English
Description
1 online resource (xxvii, 477 pages).
Item Number
10.1007/978-3-031-28949-1 doi
Call Number
QC174.4
Dewey Decimal Classification
530.13/3
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Description based on print version record.
Series
Latin American mathematics series. UFSCar subseries.
Available in Other Form
C*-ALGEBRAS AND MATHEMATICAL FOUNDATIONS OF QUANTUM STATISTICAL MECHANICS.
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Table of Contents
Preface
Ordered vector spaces and positivity
The space of bounded operators on a Hilbert space as ordered vector space
Thermodynamic equilibrium of finite quantum systems
Elements of C*-algebra
Thermodynamic equilibrium in infinite volume
Equilibrium states of mean-field models and Bogolioubov's approximation method
Appendix
References
Index.
Ordered vector spaces and positivity
The space of bounded operators on a Hilbert space as ordered vector space
Thermodynamic equilibrium of finite quantum systems
Elements of C*-algebra
Thermodynamic equilibrium in infinite volume
Equilibrium states of mean-field models and Bogolioubov's approximation method
Appendix
References
Index.