ALGEBRAIC THEORY OF SUPERSELECTION SECTORS AND THE MEASUREMENT PROBLEM IN QUANTUM MECHANICS

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Abstract
A synthesis is attempted between the algebraic theory of superselection sectors (not necessarily of infinite systems), which is based on the representation theory of C* algebras (which we review), and recent ideas on the measurement problem, classical behavior in open quantum systems, and the peculiar nature of subsystems in quantum mechanics. The key point is a proper use of the notion of a state, in combination with an appropriate choice of algebras of observables for which the superposition “principle” may be invalid. In this way, a major part of the measurement problem becomes equivalent to the study of superselection sectors in models for a measurement situation, and can in principle be resolved unambiguously. Special emphasis is placed on the transition from pure to mixed states, and the (non)uniqueness of the decomposition of the latter into pure states.

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