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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

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What are the effects of monetary policy on exchange rates? And have unconventional monetary policies changed the way monetary policy is transmitted to international financial markets? According to conventional wisdom, expansionary monetary policy shocks in a country lead to that country's currency depreciation. We revisit the conventional wisdom during both conventional and unconventional monetary policy periods in the US by using a novel identification procedure that defines monetary policy shocks as changes in the whole yield curve due to unanticipated monetary policy moves and allows monetary policy shocks to differ depending on how they affect agents' expectations about the future path of interest rates as well as their perceived effects on the riskiness/uncertainty in the economy. Our empirical results show that: (i) a monetary policy easing leads to a depreciation of the country's spot nominal exchange rate in both conventional and unconventional periods; (ii) however, there is substantial heterogeneity in monetary policy shocks over time and their effects depend on the way they affect agents' expectations; (iii) we find favorable evidence to Dornbusch's (1976) overshooting hypothesis.

Zonder onderwerpscode: economie

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Zonder onderwerpscode: financiewezen