Existence of Approximately Macroscopically Unique States

2024/02/20 by Huaxin Lin, Lin, Huaxin · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2402.12609

openalex publication_date 2024/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H be an infinite dimensional separable Hilbert space and B(H) the C*-algebra of bounded operators on H. Suppose that T₁,T₂,..., T_n are self-adjoint operators in B(H). We show that, if commutators [T_i, T_j] are sufficiently small in norm, then ``Approximately Macroscopically Unique" states always exist for any values in a synthetic spectrum of the n-tuple of self-adjoint operators. This is achieved under the circumstance for which the n-tuple may not be approximated by commuting ones. This answers a question proposed by David Mumford for measurements in quantum theory. If commutators are not small in norm but small modulo compact operators, then ``Approximate Macroscopic Uniqueness" states also exist.

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• Approximately Macroscopically Unique States and Quantum Mechanics

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