PIRSA:14040140 Scientific Series Quantum Foundations

DOI10.48660/14040140

Series: Quantum Foundations

Furber, R. (2014). Categories of Convex Sets and C*-Algebras. Perimeter Institute. https://pirsa.org/14040140

Furber, Robert. Categories of Convex Sets and C*-Algebras. Perimeter Institute, Apr. 15, 2014, https://pirsa.org/14040140 

@misc{ pirsa_PIRSA:14040140,
  doi = {10.48660/14040140},
  url = {https://pirsa.org/14040140},
  author = {Furber, Robert},
  keywords = {Quantum Foundations},
  language = {en},
  title = {Categories of Convex Sets and C*-Algebras},
  publisher = {Perimeter Institute},
  year = {2014},
  month = {apr},
  note = {PIRSA:14040140 see, \url{https://pirsa.org}}
}

Abstract

The start of the talk will be an outline how the ordinary notions of quantum theory translate into the category of C*-algebras, where there are several possible choices of morphisms. The second half will relate this to a category of convex sets used as state spaces. Alfsen and Shultz have characterized the convex sets arising from state spaces C*-algebras and this result can be applied to get a categorical equivalence between C*-algebras and state spaces of C*-algebras which is a generalization of the equivalence between the Schroedinger and Heisenberg pictures.

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