Topos Analogues of the KMS State

2012/07/01 by Joseph Ben Geloun, Geloun, Joseph Ben, Cecilia Flori +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1207.0227

openalex publication_date 2012/07/01 · arxiv created 2013/03/05 · arxiv updated 2013/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We identify the analogues of KMS state in topos theory. Topos KMS states can be viewed as classes of truth objects associated with a measure μ^ρ(in one-to-one correspondence with an original KMS state ρ) which satisfies topos condition analogues to the ordinary KMS conditions. Topos KMS states can be defined both externally or internally according to whether the automorphism group of geometric morphisms acts externally on the topos structure, or the automorphism group is an object in the topos itself, in which case, it acts internally. We illustrate the formalism by a simple example on the Hilbert space \Cl³.

Citations

• Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems
• Flows on Generalised Gelfand Spectra of Nonabelian Unital C*-Algebras and Time Evolution of Quantum Systems

Cited by

• Sheaf-Theoretic Methods in Quantum Mechanics and Quantum Information Theory

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