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@book{1836177, author = {Janyška, Josef and Modugno, Marco}, address = {Brno}, doi = {http://dx.doi.org/10.5817/CZ.MUNI.M210-8631-2022}, edition = {1., elektronické vyd.}, keywords = {universal connection; F-smooth spaces; F-smooth systems; F-smooth connections; Covariant Quantum Mechanics; quantum bundle; upper quantum connection; system of observed quantum connections; sectional quantum bundle; Schroedinger operator}, howpublished = {elektronická verze "online"}, language = {eng}, location = {Brno}, isbn = {978-80-210-8631-9}, publisher = {Masarykova univerzita}, title = {Smooth and F-smooth systems with applications to Covariant Quantum Mechanics}, year = {2022} }
TY - BOOK ID - 1836177 AU - Janyška, Josef - Modugno, Marco PY - 2022 TI - Smooth and F-smooth systems with applications to Covariant Quantum Mechanics VL - Folia Facultatis Scientiarum Naturalium Universitatis Masarykianae Brunensia, Mathematica 20 PB - Masarykova univerzita CY - Brno SN - 9788021086319 KW - universal connection KW - F-smooth spaces KW - F-smooth systems KW - F-smooth connections KW - Covariant Quantum Mechanics KW - quantum bundle KW - upper quantum connection KW - system of observed quantum connections KW - sectional quantum bundle KW - Schroedinger operator N2 - We review the geometric theory of smooth systems of smooth maps, of smooth systems of smooth sections of a smooth double bred manifold and of smooth systems of smooth connections of a smooth bred manifold. Moreover, after reviewing the concept of F{smooth space due to A. Frolicher, we discuss the F{smooth systems of smooth maps, the F{smooth systems of brewisely smooth sections of a smooth double bred manifold, the F{smooth systems of brewisely smooth connections of a smooth bred manifold and of F{smooth connections of an F{smooth system of brewisely smooth sections. Further, we discuss three applications of the general geometric theory, which are taken in the framework of Covariant Quantum Mechanics. Namely, we discuss the smooth upper quantum connection, the F{smooth sectional quantum bundle and the Schrodinger operator regarded as an F{smooth connection of the F{smooth sectional quantum bundle. ER -
JANYŠKA, Josef a Marco MODUGNO. \textit{Smooth and F-smooth systems with applications to Covariant Quantum Mechanics}. Online. 1., elektronické vyd. Brno: Masarykova univerzita, 2022, 128 s. Folia Facultatis Scientiarum Naturalium Universitatis Masarykianae Brunensia, Mathematica 20. ISBN~978-80-210-8631-9. Dostupné z: https://dx.doi.org/10.5817/CZ.MUNI.M210-8631-2022.
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