Categories of Convex Sets and C*-Algebras
APA
Furber, R. (2014). Categories of Convex Sets and C*-Algebras. Perimeter Institute. https://pirsa.org/14040140
MLA
Furber, Robert. Categories of Convex Sets and C*-Algebras. Perimeter Institute, Apr. 15, 2014, https://pirsa.org/14040140
BibTex
@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}} }
Radboud Universiteit Nijmegen
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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.