2017/09/26 by Stanisław Szawiel, Szawiel, Stanisław
Chemistry · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Category Theory (math.CT) #Chemical Thermodynamics and Molecular Structure #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.1709.09096
openalex publication_date 2017/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the mathematical foundations of physics. We reconstruct textbook quantum theory from a single symmetric monoidal functor GNS : Phys \longrightarrow \astMod, based on the Gelfand-Naimark-Segal construction and the notion of representability. We derive the probabilistic interpretation of quantum mechanics, including the Born rule, the Schrödinger and Heisenberg pictures, the relation between symmetries and group representations, and a theory of quantum Markov processes, including wave function collapse. Inclusion of the classical limit and deformation quantization is briefly sketched. Gauge symmetry and extended locality cannot currently be accommodated, due to conceptual difficulties discussed in an appendix.