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1 Fundamental assumptions -- 2 The state of a quantum system as a subsystem of a composite system -- 3 Relation between the state of a system as isolated and as open -- 4 Universality of the probability function -- 5 Appendix A -- 6 Appendix B -- 7 Appendix C -- 8 Appendix D., This book presents a selection of Prof. Matteo Campanella’s writings on the interpretative aspects of quantum mechanics and on a possible derivation of Born's rule – one of the key principles of the probabilistic interpretation of quantum mechanics – that is independent of any priori probabilistic interpretation. This topic is of fundamental interest, and as such is currently an active area of research. Starting from a natural method of defining such a state, Campanella found that it can be characterized through a partial density operator, which occurs as a consequence of the formalism and of a number of reasonable assumptions connected with the notion of a state. The book demonstrates that the density operator arises as an orbit invariant that has to be interpreted as probabilistic, and that its quantitative implementation is equivalent to Born's rule. The appendices present various mathematical details, which would have interrupted the continuity of the discussion if they had been included in the main text. For instance, they discuss baricentric coordinates, mapping between Hilbert spaces, tensor products between linear spaces, orbits of vectors of a linear space under the action of its structure group, and the class of Hilbert space as a category. |
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Campanella, Matteo 1947-2016 VerfasserIn (DE-588)121996963X (DE-627)1736073567 aut, Interpretative aspects of quantum mechanics Matteo Campanella's mathematical studies Matteo Campanella, David Jou, Maria Stella Mongiovì, Cham, Switzerland Springer Nature [2020], Palermo Università degli Studi di Palermo [2020], xv, 143 Seiten, Text txt rdacontent, ohne Hilfsmittel zu benutzen n rdamedia, Band nc rdacarrier, UNIPA Springer series, Literaturverzeichnis: Seite 131-143, 1 Fundamental assumptions -- 2 The state of a quantum system as a subsystem of a composite system -- 3 Relation between the state of a system as isolated and as open -- 4 Universality of the probability function -- 5 Appendix A -- 6 Appendix B -- 7 Appendix C -- 8 Appendix D., This book presents a selection of Prof. Matteo Campanella’s writings on the interpretative aspects of quantum mechanics and on a possible derivation of Born's rule – one of the key principles of the probabilistic interpretation of quantum mechanics – that is independent of any priori probabilistic interpretation. This topic is of fundamental interest, and as such is currently an active area of research. Starting from a natural method of defining such a state, Campanella found that it can be characterized through a partial density operator, which occurs as a consequence of the formalism and of a number of reasonable assumptions connected with the notion of a state. The book demonstrates that the density operator arises as an orbit invariant that has to be interpreted as probabilistic, and that its quantitative implementation is equivalent to Born's rule. The appendices present various mathematical details, which would have interrupted the continuity of the discussion if they had been included in the main text. For instance, they discuss baricentric coordinates, mapping between Hilbert spaces, tensor products between linear spaces, orbits of vectors of a linear space under the action of its structure group, and the class of Hilbert space as a category., Mathematical physics., Quantum physics., s (DE-588)4047989-4 (DE-627)106192728 (DE-576)209075635 Quantenmechanik gnd, s (DE-588)4072905-9 (DE-627)10609386X (DE-576)209188618 Interpretation gnd, (DE-627), Jou, David 1953- VerfasserIn (DE-588)129374679 (DE-627)393745201 (DE-576)297627589 aut, Mongiovì, Maria Stella VerfasserIn (DE-588)1229443320 (DE-627)1751417581 aut, 9783030442071, Erscheint auch als Online-Ausgabe Campanella, Matteo, 1947 - 2016 Interpretative aspects of quantum mechanics Cham : Springer, 2020 1 Online-Ressource (XV, 143 Seiten) (DE-627)1728470064 9783030442071, https://swbplus.bsz-bw.de/bsz1728470064cov.jpg V:DE-576 X:SPRINGER image/jpeg 20200917175825 Cover, https://www.gbv.de/dms/tib-ub-hannover/1736072501.pdf V:DE-601 B:DE-89 pdf/application Inhaltsverzeichnis, https://www.zbmath.org/?q=an%3A07201772 zbMATH Review, DE-Zi4 epn:3810437131 2020-12-17T14:41:30Z |
| spellingShingle |
Campanella, Matteo, Jou, David, Mongiovì, Maria Stella, Interpretative aspects of quantum mechanics: Matteo Campanella's mathematical studies, 1 Fundamental assumptions -- 2 The state of a quantum system as a subsystem of a composite system -- 3 Relation between the state of a system as isolated and as open -- 4 Universality of the probability function -- 5 Appendix A -- 6 Appendix B -- 7 Appendix C -- 8 Appendix D., This book presents a selection of Prof. Matteo Campanella’s writings on the interpretative aspects of quantum mechanics and on a possible derivation of Born's rule – one of the key principles of the probabilistic interpretation of quantum mechanics – that is independent of any priori probabilistic interpretation. This topic is of fundamental interest, and as such is currently an active area of research. Starting from a natural method of defining such a state, Campanella found that it can be characterized through a partial density operator, which occurs as a consequence of the formalism and of a number of reasonable assumptions connected with the notion of a state. The book demonstrates that the density operator arises as an orbit invariant that has to be interpreted as probabilistic, and that its quantitative implementation is equivalent to Born's rule. The appendices present various mathematical details, which would have interrupted the continuity of the discussion if they had been included in the main text. For instance, they discuss baricentric coordinates, mapping between Hilbert spaces, tensor products between linear spaces, orbits of vectors of a linear space under the action of its structure group, and the class of Hilbert space as a category., Mathematical physics., Quantum physics., Quantenmechanik, Interpretation |
| title |
Interpretative aspects of quantum mechanics: Matteo Campanella's mathematical studies |
| title_auth |
Interpretative aspects of quantum mechanics Matteo Campanella's mathematical studies |
| title_full |
Interpretative aspects of quantum mechanics Matteo Campanella's mathematical studies Matteo Campanella, David Jou, Maria Stella Mongiovì |
| title_fullStr |
Interpretative aspects of quantum mechanics Matteo Campanella's mathematical studies Matteo Campanella, David Jou, Maria Stella Mongiovì |
| title_full_unstemmed |
Interpretative aspects of quantum mechanics Matteo Campanella's mathematical studies Matteo Campanella, David Jou, Maria Stella Mongiovì |
| title_short |
Interpretative aspects of quantum mechanics |
| title_sort |
interpretative aspects of quantum mechanics matteo campanella's mathematical studies |
| title_sub |
Matteo Campanella's mathematical studies |
| title_unstemmed |
Interpretative aspects of quantum mechanics: Matteo Campanella's mathematical studies |
| topic |
Mathematical physics., Quantum physics., Quantenmechanik, Interpretation |
| topic_facet |
Mathematical physics., Quantum physics., Quantenmechanik, Interpretation |
| url |
https://swbplus.bsz-bw.de/bsz1728470064cov.jpg, https://www.gbv.de/dms/tib-ub-hannover/1736072501.pdf, https://www.zbmath.org/?q=an%3A07201772 |
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