caa a22 4500 467906629 CHVBK 20180406152836.0 cr unu---uuuuu 170328e20060201xx s 000 0 eng 10.1007/s10701-005-9012-1 doi (NATIONALLICENCE)springer-10.1007/s10701-005-9012-1 Kryukov Alexey Department of Mathematics, University of Wisconsin Colleges, 780 Regent Street, 53708, Madison, WI, USA aut Quantum Mechanics on Hilbert Manifolds: The Principle of Functional Relativity [Elektronische Daten] [Alexey Kryukov] Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this setting, also called functional tensor equations, describe families of functional equations on various Hilbert spaces of functions. The principle of functional relativity is introduced which states that quantum theory (QT) is indeed a functional tensor theory, i.e., it can be described by functional tensor equations. The main equations of QT are shown to be compatible with the principle of functional relativity. By accepting the principle as a hypothesis, we then explain the origin of physical dimensions, provide a geometric interpretation of Planck's constant, and find a simple model of the two-slit experiment and the process of measurement. Springer Science+Business Media, Inc., 2006 space-time nationallicence emergence nationallicence measurement problem nationallicence generalized functions nationallicence Hilbert manifolds nationallicence Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/2(2006-02-01), 175-226 0015-9018 36:2<175 2006 36 10701 https://doi.org/10.1007/s10701-005-9012-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10701-005-9012-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kryukov Alexey Department of Mathematics, University of Wisconsin Colleges, 780 Regent Street, 53708, Madison, WI, USA aut NATIONALLICENCE 773 0- Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/2(2006-02-01), 175-226 0015-9018 36:2<175 2006 36 10701 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer