Operator Algebras and Quantum Statistical Mechanics: Equilibrium States. Models in Quantum Statistical MechanicsFor almost two decades this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. It describes the general structure of equilibrium states, the KMS-condition and stability, quantum spin systems and continuous systems. Major changes in the new edition relate to Bose--Einstein condensation, the dynamics of the X-Y model and questions on phase transitions. Notes and remarks have been considerably augmented. |
Contents
| 3 | |
Notes and Remarks | 40 |
Groups Semigroups and Generators | 157 |
CAlgebras and von Neumann Algebras | 204 |
Notes and Remarks | 217 |
Notes and Remarks | 298 |
Decomposition Theory | 309 |
Notes and Remarks | 424 |
Notes and Remarks | 451 |
References | 459 |
References | 463 |
Articles 464 | 468 |
| 481 | |
List of Symbols | 487 |
| 499 | |
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Common terms and phrases
assume asymptotic abelianness automorphism group Bogoliubov Bogoliubov transformations boundary conditions bounded C*-algebra C*-dynamical system CCR algebra commutation convergence convex Corollary corresponding decomposition defined denote dense density Dirichlet dynamics eigenvalues elements energy entropy equilibrium ergodic Example exists extremal finite Fock space follows function ground group of automorphisms Hamiltonian hence Hilbert space identity implies inequality interaction Ising model KMS condition L²(R lattice Lemma linear matrix measure modular Moreover Neumann algebra norm Notes and Remarks Observation one-parameter group P₁ particles perturbation positive proof of Theorem properties Proposition prove quantum spin quantum spin system quasi-free relation representation satisfies selfadjoint selfadjoint operator space h stability strongly continuous subalgebra subset subspace symmetry t-invariant t-KMS T₁ temperature thermodynamic limit topology trace-class unique unitary value ẞ vector von Neumann algebra w₁ w₂