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Tomita–Takesaki Modular Theory: From Locality to Thermality

Lecturer
Ricardo Correa da Silva (IFUSP, Brazil)
Language
English
Schedule
27–30 Jul 2026 (4 classes)
Time
09h00 (BRT)/12h00 (UTC)
Workload
8h
Topics
  • Lecture 1
    • Review on unbounded linear and antilinear operator on Hilbert spaces and their polar decomposition
    • Nets of local algebras and the Reeh–Schlieder Theorem
  • Lecture 2
    • Von Neumann algebras with cyclic and separating vectors
    • Standard subspaces
    • The Tomita operator and its properties
  • Lecture 3
    • The Tomita–Takesaki Theorem
    • KMS States
    • Physical examples in Modular Theory
  • Lecture 4
    • The Bisognano–Wichman Theorem
    • Relative modular theory and Araki's relative entropy