LEADER 03432nam 22005655 450 001 9910483467703321 005 20251113185209.0 010 $a3-030-44207-1 024 7 $a10.1007/978-3-030-44207-1 035 $a(CKB)4100000011401193 035 $a(MiAaPQ)EBC6320905 035 $a(DE-He213)978-3-030-44207-1 035 $a(PPN)250215993 035 $a(MiAaPQ)EBC6320747 035 $a(EXLCZ)994100000011401193 100 $a20200827d2020 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aInterpretative Aspects of Quantum Mechanics $eMatteo Campanella's Mathematical Studies /$fby Matteo Campanella, David Jou, Maria Stella Mongiovì 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (153 pages) $cillustrations 225 1 $aUNIPA Springer Series,$x2366-7524 300 $aIncludes index. 311 08$a3-030-44206-3 327 $a1 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. 330 $aThis book presents a selection of Prof. Matteo Campanella?s writings on the interpretative aspects of quantum mechanics and on a possible derivation of Born's rule ? one of the key principles of the probabilistic interpretation of quantum mechanics ? that is independent of any priori probabilistic interpretation. This topic is of fundamental interest, and as such is currently an active area of research. Starting from a natural method of defining such a state, Campanella found that it can be characterized through a partial density operator, which occurs as a consequence of the formalism and of a number of reasonable assumptions connected with the notion of a state. The book demonstrates that the density operator arises as an orbit invariant that has to be interpreted as probabilistic, and that its quantitative implementation is equivalent to Born's rule. The appendices present various mathematical details, which would have interrupted the continuity of the discussion if they had been included in the main text. For instance, they discuss baricentric coordinates, mapping between Hilbert spaces, tensor products between linear spaces, orbits of vectors of a linear space under the action of its structure group, and the class of Hilbert space as a category. 410 0$aUNIPA Springer Series,$x2366-7524 606 $aMathematical physics 606 $aQuantum theory 606 $aMathematical Physics 606 $aQuantum Physics 615 0$aMathematical physics. 615 0$aQuantum theory. 615 14$aMathematical Physics. 615 24$aQuantum Physics. 676 $a530.12 700 $aCampanella$b Matteo$4aut$4http://id.loc.gov/vocabulary/relators/aut$0977150 702 $aJou$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aMongiovì$b Maria Stella$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483467703321 996 $aInterpretative Aspects of Quantum Mechanics$92226056 997 $aUNINA