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

Tags

Readers

  • Mathematical Modeling and Probability Theory.
  • Theoretical Analysis.
  • Wave Propagation and Nonlinear Chaotic Dynamics.

Technology Areas

  • Quantum Computing
  • Space