Modular action on the massive algebra [Elektronische Ressource] / vorgelegt von Timor Saffary

Modular Actionon the Massive AlgebraDissertationzur Erlangung des Doktorgradesdes Fachbereichs Physikder Universit at Hamburgvorgelegt vonTimor Sa aryaus Kabul, AfghanistanHamburg 2005Gutachter der Dissertation: Prof. Dr. K. FredenhagenProf. Dr. G. MackGutachter der Disputation: Prof. Dr. K. FredenhagenDr. V. SchomerusDatum der Disputation: 12. Dezember 2005Vorsitzender des Prufungsaussc husses: Prof. Dr. J. BarthelsV des Promotionsausschusses: Prof. Dr. G. HuberDekan des Fachbereichs Physik: Prof. Dr. G. HuberFor my parentsSha k a and Sohrab Ali Sa aryModular Action on the Massive AlgebraAbstract: tThe subject of this thesis is the modular group of automorphisms ,m t2Rm> 0, acting on the massive algebra of local observables M (O) having theirm4support in O R . After a compact introduction to micro-local analysis andthe theory of one-parameter groups of automorphisms, which are used exen-sively throughout the investigation, we are concerned with modular theory andits consequences in mathematics, e.g., Connes’ cocycle theorem and classi ca-tion of type III factors and Jones’ index theory, as well as in physics, e.g.,the determination of local von Neumann algebras to be hyper nite factors oftype III , the formulation of thermodynamic equilibrium states for in nite-1dimensional quantum systems (KMS states) and the discovery of modular ac-tion as geometric transformations.