Quantum States and Measures on the Spectral Presheaf - Quantum PhysicsReport as inadecuate




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Abstract: After a brief introduction to the spectral presheaf, which serves as ananalogue of state space in the topos approach to quantum theory, we show thatevery state of the von Neumann algebra of physical quantities of a quantumsystem determines a certain measure on the spectral presheaf of the system. Theso-called clopen subobjects of the spectral presheaf play the role ofmeasurable sets. Measures on the spectral presheaf can be characterisedabstractly, and the main result is that every abstract measure induces a uniquestate of the von Neumann algebra. Finally, we show how quantum-theoreticalexpectation values can be calculated from measures associated to quantumstates.



Author: A. Doering

Source: https://arxiv.org/



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