2005/10/08 by Don Ridgeway, Ridgeway, Don
Mathematics · Physics and Astronomy · #46A13 (primary) #46M40 (secondary) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:46A13 #msc:46M40
paper · pdf · doi:10.48550/arxiv.math-ph/0510031
10 pages, latex amsart
arxiv created 2005/10/08 · arxiv updated 2009/12/01
We apply the algebraic theory of infinite classical lattices from Part I to write an axiomatic theory of measurements, based on Mackey's axioms for quantum mechanics. The axioms give a complete theory of measurements in the sense of Haag and Kastler, taking the traditional form of a logic of propositions provided with a classical spectral theorem. The results are expressed in terms of probability distributions of individual measurements. As applications, we give a separation theorem for states by the set of observables and discuss its relationship to the equivalence of ensembles in the thermodynamic-limit program. We also introduce a weak equivalence of states based on the theory.