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An algebraic theory of infinite classical lattices II: Axiomatic theory

Don Ridgeway
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Abstract

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.

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Don Ridgeway. 2005-10-08. An algebraic theory of infinite classical lattices II: Axiomatic theory. https://arxiv.org/abs/math-ph/0510031

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