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Topics in the mathematics of quantum mechanics

Course Type: 
PhD Course
Academic Year: 
2014-2015
Period: 
From October 17
Duration: 
20 h
Description: 

Topicsa selection of the following material, based upon the participants' background

  • Historical remarks, axioms, Schroedinger’s and Heisenberg’s formulations, difficulties (decoherence, measurement, ..), Bell’s inequalities, alternative theories.
  • Kinematics: mapping of states, homeomorphism of observables (theorems of Wigner, Kadison, Segal), continuity. evolution described by one parameter group of unitaries.
  • Comparison with Hamiltonian dynamics The problem of quantisation.
  • Operators in Hilbert spaces: basic facts.
  • Analytic solution for free motion. Propagation (Strichartz) inequalities. Anholonomy.
  • Elements of C*-algebras, GNS representation, automorphism and dynamical systems.
  • Quantisation: Weyl's system and Weyl's algebra. Representations of Bargmann-Segal, Fock, Berezin.

 

Undergrad pre-requisites: basics of Quantum Mechanics (familiarity not requried) 

Main references (graduate texts)G. Dell'Antonio, Mathematical Aspects of Quantum Mechanics. Volume 1 (2011). Available online in the form of lecture notes both in English and in Italian. An enlarged version of the English edition is in preparation.

 

Examexposition and discussion in class of an assigned research paper (or of an assigned textbook chapter)

Location: 
Room 134 on Tuesdays, Room 136 on Fridays
Next Lectures: 

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