An algebraic theory of infinite classical lattices II: Axiomatic theory

Details An algebraic theory of infinite classical lattices II: Axiomatic theory An algebraic theory of infinite classical lattices II: Axiomatic theory

2005-10-08

arxiv.org/abs/math-ph/0510031v1

Physics

Mathematical Physics

10 pages, latex amsart

Scientific paper

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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