Axioms of Quantum Mechanics in light of Continuous Model Theory

2025/05/30 by Boris Zilber, Zilber, Boris · 1 citation
Physics and Astronomy · #03C66 #81P10 #FOS: Mathematics #FOS: Physical sciences #Logic (math.LO) #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2506.02029

openalex publication_date 2025/05/30 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

The aim of this note is to recast somewhat informal axiom system of quantum mechanics used by physicists (Dirac calculus) in the language of Continuous Logic. We note an analogy between Tarski's notion of cylindric algebras, as a tool of algebraisation of first order logic, and Hilbert spaces which can serve the same purpose for continuous logic of physics.

Citations

• Dirac - von Neumann axioms in the setting of Continuous Model Theory
• An Introduction To Continuous Model Theory
• The role of the rigged Hilbert space in quantum mechanics

Cited by

• Dirac - von Neumann axioms in the setting of Continuous Model Theory

Related

• Dirac - von Neumann axioms in the setting of Continuous Model Theory
• Dirac Book The Principles Of Quantum Mechanics as presenting the alternative organization of a theory
• Postulates of quantum mechanics and phenomenology
• On the logical structure of physics
• Seven Principles of Quantum Mechanics