Gleason's Theorem and Its Applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1993
|
| Schriftenreihe: | Mathematics and Its Applications, East European Series
60 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | For many years physics and mathematics have had a fruitful influence on one another. Classical mechanics and celestial mechanics have produced very deep problems whose solutions have enhanced mathematics. On the other hand, mathematics itself has found interesting theories which then (sometimes after many years) have been reflected in physics, confirming the thesis that nothing is more practical than a good theory. The same is true for the younger physical discipline -of quantum mechanics. In the 1930s two events, not at all random, became: The mathematical back grounds of both quantum mechanics and probability theory. In 1936, G. Birkhoff and J. von Neumann published their historical paper "The logic of quantum mechanics", in which a quantum logic was suggested. The mathematical foundations of quantum mechanics remains an outstanding problem of mathematics, physics, logic and philosophy even today. The theory of quantum logics is a major stream in this axiomatical knowledge river, where L(H), the system of all closed subspaces of a Hilbert space H, due to J. von Neumann, plays an important role. When A.M. Gleason published his solution to G. Mackey's problem showing that any state (= probability measure) corresponds to a density operator, he probably did not anticipate that his solution would become a cornerstone of ax iomati cal theory of quantum mechanics nor that it would provide many interesting applications to mathematics |
| Beschreibung: | 1 Online-Ressource (XVI, 325 p) |
| ISBN: | 9789401582223 9789048142095 |
| ISSN: | 0169-507X |
| DOI: | 10.1007/978-94-015-8222-3 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042424043 | ||
| 003 | DE-604 | ||
| 005 | 20160616 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1993 |||| o||u| ||||||eng d | ||
| 020 | |a 9789401582223 |c Online |9 978-94-015-8222-3 | ||
| 020 | |a 9789048142095 |c Print |9 978-90-481-4209-5 | ||
| 024 | 7 | |a 10.1007/978-94-015-8222-3 |2 doi | |
| 035 | |a (OCoLC)863945168 | ||
| 035 | |a (DE-599)BVBBV042424043 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 515.42 |2 23 | |
| 084 | |a PHY 011f |2 stub | ||
| 084 | |a MAT 472f |2 stub | ||
| 084 | |a MAT 000 |2 stub | ||
| 084 | |a MAT 039f |2 stub | ||
| 100 | 1 | |a Dvurečenskij, Anatolij |d 1949- |e Verfasser |0 (DE-588)172681979 |4 aut | |
| 245 | 1 | 0 | |a Gleason's Theorem and Its Applications |c by Anatolij Dvurečenskij |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 1993 | |
| 300 | |a 1 Online-Ressource (XVI, 325 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Mathematics and Its Applications, East European Series |v 60 |x 0169-507X | |
| 500 | |a For many years physics and mathematics have had a fruitful influence on one another. Classical mechanics and celestial mechanics have produced very deep problems whose solutions have enhanced mathematics. On the other hand, mathematics itself has found interesting theories which then (sometimes after many years) have been reflected in physics, confirming the thesis that nothing is more practical than a good theory. The same is true for the younger physical discipline -of quantum mechanics. In the 1930s two events, not at all random, became: The mathematical back grounds of both quantum mechanics and probability theory. In 1936, G. Birkhoff and J. von Neumann published their historical paper "The logic of quantum mechanics", in which a quantum logic was suggested. The mathematical foundations of quantum mechanics remains an outstanding problem of mathematics, physics, logic and philosophy even today. The theory of quantum logics is a major stream in this axiomatical knowledge river, where L(H), the system of all closed subspaces of a Hilbert space H, due to J. von Neumann, plays an important role. When A.M. Gleason published his solution to G. Mackey's problem showing that any state (= probability measure) corresponds to a density operator, he probably did not anticipate that his solution would become a cornerstone of ax iomati cal theory of quantum mechanics nor that it would provide many interesting applications to mathematics | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Quantum theory | |
| 650 | 4 | |a Measure and Integration | |
| 650 | 4 | |a Applications of Mathematics | |
| 650 | 4 | |a Quantum Physics | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 0 | 7 | |a Maßtheorie |0 (DE-588)4074626-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantenlogik |0 (DE-588)4176599-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hilbert-Raum |0 (DE-588)4159850-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lineares Funktional |0 (DE-588)4167728-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hilbert-Raum |0 (DE-588)4159850-7 |D s |
| 689 | 0 | 1 | |a Lineares Funktional |0 (DE-588)4167728-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Quantenlogik |0 (DE-588)4176599-0 |D s |
| 689 | 1 | 1 | |a Maßtheorie |0 (DE-588)4074626-4 |D s |
| 689 | 1 | |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-94-015-8222-3 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027859460 | ||
Datensatz im Suchindex
| _version_ | 1804153100497321984 |
|---|---|
| any_adam_object | |
| author | Dvurečenskij, Anatolij 1949- |
| author_GND | (DE-588)172681979 |
| author_facet | Dvurečenskij, Anatolij 1949- |
| author_role | aut |
| author_sort | Dvurečenskij, Anatolij 1949- |
| author_variant | a d ad |
| building | Verbundindex |
| bvnumber | BV042424043 |
| classification_tum | PHY 011f MAT 472f MAT 000 MAT 039f |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863945168 (DE-599)BVBBV042424043 |
| dewey-full | 515.42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.42 |
| dewey-search | 515.42 |
| dewey-sort | 3515.42 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1007/978-94-015-8222-3 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03520nmm a2200601zcb4500</leader><controlfield tag="001">BV042424043</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20160616 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1993 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789401582223</subfield><subfield code="c">Online</subfield><subfield code="9">978-94-015-8222-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789048142095</subfield><subfield code="c">Print</subfield><subfield code="9">978-90-481-4209-5</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-94-015-8222-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863945168</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042424043</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.42</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">PHY 011f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 472f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 039f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dvurečenskij, Anatolij</subfield><subfield code="d">1949-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)172681979</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Gleason's Theorem and Its Applications</subfield><subfield code="c">by Anatolij Dvurečenskij</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht</subfield><subfield code="b">Springer Netherlands</subfield><subfield code="c">1993</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XVI, 325 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Mathematics and Its Applications, East European Series</subfield><subfield code="v">60</subfield><subfield code="x">0169-507X</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">For many years physics and mathematics have had a fruitful influence on one another. Classical mechanics and celestial mechanics have produced very deep problems whose solutions have enhanced mathematics. On the other hand, mathematics itself has found interesting theories which then (sometimes after many years) have been reflected in physics, confirming the thesis that nothing is more practical than a good theory. The same is true for the younger physical discipline -of quantum mechanics. In the 1930s two events, not at all random, became: The mathematical back grounds of both quantum mechanics and probability theory. In 1936, G. Birkhoff and J. von Neumann published their historical paper "The logic of quantum mechanics", in which a quantum logic was suggested. The mathematical foundations of quantum mechanics remains an outstanding problem of mathematics, physics, logic and philosophy even today. The theory of quantum logics is a major stream in this axiomatical knowledge river, where L(H), the system of all closed subspaces of a Hilbert space H, due to J. von Neumann, plays an important role. When A.M. Gleason published his solution to G. Mackey's problem showing that any state (= probability measure) corresponds to a density operator, he probably did not anticipate that his solution would become a cornerstone of ax iomati cal theory of quantum mechanics nor that it would provide many interesting applications to mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Quantum theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Measure and Integration</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Applications of Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Quantum Physics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Quantentheorie</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Maßtheorie</subfield><subfield code="0">(DE-588)4074626-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Quantenlogik</subfield><subfield code="0">(DE-588)4176599-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Hilbert-Raum</subfield><subfield code="0">(DE-588)4159850-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lineares Funktional</subfield><subfield code="0">(DE-588)4167728-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Hilbert-Raum</subfield><subfield code="0">(DE-588)4159850-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Lineares Funktional</subfield><subfield code="0">(DE-588)4167728-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Quantenlogik</subfield><subfield code="0">(DE-588)4176599-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Maßtheorie</subfield><subfield code="0">(DE-588)4074626-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-94-015-8222-3</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027859460</subfield></datafield></record></collection> |
| id | DE-604.BV042424043 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401582223 9789048142095 |
| issn | 0169-507X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859460 |
| oclc_num | 863945168 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XVI, 325 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer Netherlands |
| record_format | marc |
| series2 | Mathematics and Its Applications, East European Series |
| spelling | Dvurečenskij, Anatolij 1949- Verfasser (DE-588)172681979 aut Gleason's Theorem and Its Applications by Anatolij Dvurečenskij Dordrecht Springer Netherlands 1993 1 Online-Ressource (XVI, 325 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications, East European Series 60 0169-507X For many years physics and mathematics have had a fruitful influence on one another. Classical mechanics and celestial mechanics have produced very deep problems whose solutions have enhanced mathematics. On the other hand, mathematics itself has found interesting theories which then (sometimes after many years) have been reflected in physics, confirming the thesis that nothing is more practical than a good theory. The same is true for the younger physical discipline -of quantum mechanics. In the 1930s two events, not at all random, became: The mathematical back grounds of both quantum mechanics and probability theory. In 1936, G. Birkhoff and J. von Neumann published their historical paper "The logic of quantum mechanics", in which a quantum logic was suggested. The mathematical foundations of quantum mechanics remains an outstanding problem of mathematics, physics, logic and philosophy even today. The theory of quantum logics is a major stream in this axiomatical knowledge river, where L(H), the system of all closed subspaces of a Hilbert space H, due to J. von Neumann, plays an important role. When A.M. Gleason published his solution to G. Mackey's problem showing that any state (= probability measure) corresponds to a density operator, he probably did not anticipate that his solution would become a cornerstone of ax iomati cal theory of quantum mechanics nor that it would provide many interesting applications to mathematics Mathematics Quantum theory Measure and Integration Applications of Mathematics Quantum Physics Mathematik Quantentheorie Maßtheorie (DE-588)4074626-4 gnd rswk-swf Quantenlogik (DE-588)4176599-0 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Lineares Funktional (DE-588)4167728-6 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 s Lineares Funktional (DE-588)4167728-6 s DE-604 Quantenlogik (DE-588)4176599-0 s Maßtheorie (DE-588)4074626-4 s https://doi.org/10.1007/978-94-015-8222-3 Verlag Volltext |
| spellingShingle | Dvurečenskij, Anatolij 1949- Gleason's Theorem and Its Applications Mathematics Quantum theory Measure and Integration Applications of Mathematics Quantum Physics Mathematik Quantentheorie Maßtheorie (DE-588)4074626-4 gnd Quantenlogik (DE-588)4176599-0 gnd Hilbert-Raum (DE-588)4159850-7 gnd Lineares Funktional (DE-588)4167728-6 gnd |
| subject_GND | (DE-588)4074626-4 (DE-588)4176599-0 (DE-588)4159850-7 (DE-588)4167728-6 |
| title | Gleason's Theorem and Its Applications |
| title_auth | Gleason's Theorem and Its Applications |
| title_exact_search | Gleason's Theorem and Its Applications |
| title_full | Gleason's Theorem and Its Applications by Anatolij Dvurečenskij |
| title_fullStr | Gleason's Theorem and Its Applications by Anatolij Dvurečenskij |
| title_full_unstemmed | Gleason's Theorem and Its Applications by Anatolij Dvurečenskij |
| title_short | Gleason's Theorem and Its Applications |
| title_sort | gleason s theorem and its applications |
| topic | Mathematics Quantum theory Measure and Integration Applications of Mathematics Quantum Physics Mathematik Quantentheorie Maßtheorie (DE-588)4074626-4 gnd Quantenlogik (DE-588)4176599-0 gnd Hilbert-Raum (DE-588)4159850-7 gnd Lineares Funktional (DE-588)4167728-6 gnd |
| topic_facet | Mathematics Quantum theory Measure and Integration Applications of Mathematics Quantum Physics Mathematik Quantentheorie Maßtheorie Quantenlogik Hilbert-Raum Lineares Funktional |
| url | https://doi.org/10.1007/978-94-015-8222-3 |
| work_keys_str_mv | AT dvurecenskijanatolij gleasonstheoremanditsapplications |