Abstract
This chapter contains the quantum realization of our ideas about a mathematical description of measurements with a finite precision (see section 6 of Chapter 1). The precision of a quantum measurement is used as a new metric on the space of quantum states. This metric is an ultrametric. Thus formally our quantum model can be considered as a representation of canonical commutation relations in ultrametric Hilbert spaces.
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© 1997 Kluwer Academic Publishers
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Khrennikov, A. (1997). The Ultrametric Hilbert Space Description of Quantum Measurements with Finite Precision. In: Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models. Mathematics and Its Applications, vol 427. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1483-4_4
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DOI: https://doi.org/10.1007/978-94-009-1483-4_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7164-2
Online ISBN: 978-94-009-1483-4
eBook Packages: Springer Book Archive