von Neumann algebras and local quantum theory - Notes

Dr I F Wilde

von Neumann algebras and local quantum theory - Notes (pdf file) (and references)

These notes are based on lectures given many years ago at the Institute of Physics, University of São Paulo, Brazil.
It is a pleasure to thank Fernando Perez for kind hospitality and numerous enjoyable discussions together with Ely Belotto Silva, Cezar Bonato and Ricardo Neves da Silva.
The material includes an introduction to von Neumann algebras and modular theory and the beginnings of algebraic quantum theory.

Sections 1 and 2 follow on from the notes on C*-algebras.


  1. Operator algebras
  2. Modular theory
  3. The canonical commutation relations
  4. The algebraic approach to quantum theory
  5. Local quantum theory
  6. The charged Bose field and its sectors
  7. The general structure of sectors
  8. References

- further available material.

Ivan F Wilde
e-mail: iwilde (dot) mth (at) ntlworld (dot) com
<This page updated 14 June 2009>