Introduction to C* algebras

Dr. Gherardo Piacitelli

Number of cycles: 1

First semester: Tuesdays 2-4pm, Wednesdays 4-6pm (starting October 3)


First part (8 hours): Basics about C*-algebras and their representations.
Definition of C*-algebras, Gelfand transform, functional calculus, representation theory, GNS construction, universal representation, geometry of states. Operator algebras: weak topologies, bicommutant theorem. Tomita-Takesaki theorem (statement only)

Second Part (12 hours): selected topics in Quantum Physics.
Axioms for Quantum Physics (Copenhagen interpretation), generalised Heisenberg uncertainty ``principle'' (a theorem, actually). Localisability and Weyl relations. Von Neumann uniqueness of the Schr\"odinger representation, Weyl quantisation. The quantum harmonic oscillator (sketchy). Rotations. Elements of local (relativistic) quantum physics. Superselection theory as a duality problem for compact groups.