Jean-Bernard Bru,Walter Alberto de Siqueira Pedra
C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics: An Introduction
C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics: An Introduction
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- More about C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics: An Introduction
This textbook provides a comprehensive introduction to the mathematical foundations of quantum statistical physics, using C*-algebras to demonstrate how key aspects of thermodynamic equilibrium can be derived from classical results in convex analysis. It covers Gibbs states, thermodynamic equilibrium, and first-order phase transitions, making it suitable for mathematicians and physicists with a interest in quantum statistical physics.
Format: Hardback
Length: 477 pages
Publication date: 18 June 2023
Publisher: Springer International Publishing AG
This comprehensive textbook offers a thorough 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.
Utilizing C*-algebras as examples of ordered vector spaces, this book elucidates various aspects of C*-algebras and their applications to the mathematical foundations of quantum theory 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.
Weight: 922g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031289484
Edition number: 1st ed. 2023
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