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Hilbert space, the number of Higgs particles and the quantum two-slit experiment. (English) Zbl 1082.81501
Summary: Rigorous mathematical formulation of quantum mechanics requires the introduction of a Hilbert space. By contrast, the Cantorian E-infinity approach to quantum physics was developed largely without any direct reference to the afore mentioned mathematical spaces. In the present work we present a novel reinterpretation of basic \(\varepsilon^{(\infty)}\) Cantorian spacetime relations in terms of the Hilbert space of quantum mechanics. In this way, we gain a better understanding of the physical and mathematical structure of quantum spacetime. In particular we show that the two-slit experiment required a definite topology which is consistent with a certain fuzzy Kähler manifold or more generally a Cantorian spacetime manifold. Finally by determining the Euler class of this manifold, we can estimate the most likely number of Higgs particles which may be discovered.

81P99 Foundations, quantum information and its processing, quantum axioms, and philosophy
Full Text: DOI
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