Axioms for the category of Hilbert spaces
Abstract
Hilbert spaces and their operators are the mathematical foundation of quantum mechanics. The problem of reconstructing this foundation from first principles has been open for nearly a century. What is mathematically special about Hilbert spaces and their operators? This paper gives a categorical axiomatization. Unlike previous partial results of this type, the axioms do not presuppose probabilities, complex amplitudes, or continuity and are not limited to finite dimension.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Feb 25, 2022
- Source ID
- 10.1073/pnas.2117024119
Entities
People
- Andre Kornell
- Chris Heunen
Organizations
- Air Force Office of Scientific Research
- Engineering and Physical Sciences Research Council
- Tulane University of Louisiana
- University of Edinburgh