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Quantum field theory --- Quantum field theory. --- C*-algebras.

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Ordered algebraic structures --- 51 --- Mathematics --- C*-algebras. --- Polynomials. --- Polytopes. --- Random walks (Mathematics) --- Random walks (Mathematics). --- 51 Mathematics

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Operator theory --- Afbeeldingen (Wiskunde) --- Algèbres [C*- ] --- Applications (Mathematiques) --- C*-algebra's --- C*-algebras --- Dilation theory (Operator theory) --- Mappings (Mathematics) --- Maps (Mathematics)

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Functional analysis --- 51 --- Von Neumann algebras --- Factors (Algebra) --- Algebra --- Factorization (Mathematics) --- Algebras, Von Neumann --- Algebras, W --- Neumann algebras --- Rings of operators --- W*-algebras --- C*-algebras --- Hilbert space --- Mathematics --- Von Neumann algebras. --- Factors (Algebra). --- 51 Mathematics

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These notes are devoted to a systematic study of developing the Tomita-Takesaki theory for von Neumann algebras in unbounded operator algebras called O*-algebras and to its applications to quantum physics. The notions of standard generalized vectors and standard weights for an O*-algebra are introduced and they lead to a Tomita-Takesaki theory of modular automorphisms. The Tomita-Takesaki theory in O*-algebras is applied to quantum moment problem, quantum statistical mechanics and the Wightman quantum field theory. This will be of interest to graduate students and researchers in the field of (unbounded) operator algebras and mathematical physics.

Quantum theory --- Operator algebras --- Algèbres d'opérateurs --- Dynamique quantique --- Mécanique des quanta --- Mécanique quantique --- Operatorenalgebra's --- Quanta [Théorie des ] --- Quantum dynamics --- Quantum mechanics --- Quantumtheorie --- Théorie des quanta --- Théorie quantique --- Von Neumann [Algebra's van ] --- Von Neumann [Algèbres de ] --- Von Neumann algebras --- 51 --- 51 Mathematics --- Mathematics --- Algebras, Von Neumann --- Algebras, W --- Neumann algebras --- Rings of operators --- W*-algebras --- C*-algebras --- Hilbert space --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Algebras, Operator --- Operator theory --- Topological algebras --- 51 Wiskunde. Mathematiek --- Wiskunde. Mathematiek --- Algebra. --- Operator theory. --- Quantum physics. --- Quantum computers. --- Spintronics. --- Operator Theory. --- Quantum Physics. --- Quantum Information Technology, Spintronics. --- Fluxtronics --- Magnetoelectronics --- Spin electronics --- Spinelectronics --- Microelectronics --- Nanotechnology --- Computers --- Functional analysis --- Mathematical analysis