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020 _a9783031289484
041 _aeng
082 _a530.133
_bBruA
100 _aBru, Jean-Bernard
245 _aC*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics :
_bAn Introduction /
_cJean-Bernard Bru and Walter Alberto de Siqueira Pedra
260 _aSwitzerland:
_bSpringer;
_c©2023
300 _axxvii, 477p.
440 _aLatin American Mathematics Series
_vUFSCar subseries
520 _aThis 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.
650 _aMathematical Physics
650 _aMathematical Methods in Physics
650 _aQuantum Physics
650 _aTheoretical and Computational Chemistry
650 _aFunctional Analysis
700 _aPedra, Walter Alberto de Siqueira
942 _cBK
999 _c7166
_d7166