Indefinite Inner Product Spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1974
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete
78 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | By definition, an indefinite inner product space is a real or complex vector space together with a symmetric (in the complex case: hermi tian) bilinear form prescribed on it so that the corresponding quadratic form assumes both positive and negative values. The most important special case arises when a Hilbert space is considered as an orthogonal direct sum of two subspaces, one equipped with the original inner prod uct, and the other with -1 times the original inner product. The subject first appeared thirty years ago in a paper of Dirac [1] on quantum field theory (d. also Pauli [lJ). Soon afterwards, Pontrja gin [1] gave the first mathematical treatment of an indefinite inner prod uct space. Pontrjagin was unaware of the investigations of Dirac and Pauli; on the other hand, he was inspired by a work of Sobolev [lJ, unpublished up to 1960, concerning a problem of mechanics. The attempts of Dirac and Pauli to apply the concept and elemen tary properties of indefinite inner product spaces to field theory have been renewed by several authors. At present it is not easy to judge which of their results will contribute to the final form of this part of physics. The following list of references should serve as a guide to the extensive literature: Bleuler [1], Gupta [lJ, Kallen and Pauli [lJ, Heisen berg [lJ-[4J, Bogoljubov, Medvedev and Polivanov [lJ, K.L.Nagy [lJ-[3], Berezin [lJ, Arons, Han and Sudarshan [1], Lee and Wick [1J. |
| Beschreibung: | 1 Online-Ressource (X, 226 p) |
| ISBN: | 9783642655678 9783642655692 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-642-65567-8 |
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Bognár, János |
| author_facet | Bognár, János |
| author_role | aut |
| author_sort | Bognár, János |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-65567-8 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642655678 9783642655692 |
| issn | 0071-1136 |
| language | English |
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| spelling | Bognár, János Verfasser aut Indefinite Inner Product Spaces by János Bognár Berlin, Heidelberg Springer Berlin Heidelberg 1974 1 Online-Ressource (X, 226 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 78 0071-1136 By definition, an indefinite inner product space is a real or complex vector space together with a symmetric (in the complex case: hermi tian) bilinear form prescribed on it so that the corresponding quadratic form assumes both positive and negative values. The most important special case arises when a Hilbert space is considered as an orthogonal direct sum of two subspaces, one equipped with the original inner prod uct, and the other with -1 times the original inner product. The subject first appeared thirty years ago in a paper of Dirac [1] on quantum field theory (d. also Pauli [lJ). Soon afterwards, Pontrja gin [1] gave the first mathematical treatment of an indefinite inner prod uct space. Pontrjagin was unaware of the investigations of Dirac and Pauli; on the other hand, he was inspired by a work of Sobolev [lJ, unpublished up to 1960, concerning a problem of mechanics. The attempts of Dirac and Pauli to apply the concept and elemen tary properties of indefinite inner product spaces to field theory have been renewed by several authors. At present it is not easy to judge which of their results will contribute to the final form of this part of physics. The following list of references should serve as a guide to the extensive literature: Bleuler [1], Gupta [lJ, Kallen and Pauli [lJ, Heisen berg [lJ-[4J, Bogoljubov, Medvedev and Polivanov [lJ, K.L.Nagy [lJ-[3], Berezin [lJ, Arons, Han and Sudarshan [1], Lee and Wick [1J. Mathematics Mathematics, general Mathematik Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Indefinites Skalarprodukt (DE-588)4161471-9 gnd rswk-swf Raum Mathematik (DE-588)4124030-3 gnd rswk-swf Produktraum (DE-588)4130367-2 gnd rswk-swf Produktraum (DE-588)4130367-2 s 1\p DE-604 Funktionalanalysis (DE-588)4018916-8 s 2\p DE-604 Indefinites Skalarprodukt (DE-588)4161471-9 s 3\p DE-604 Raum Mathematik (DE-588)4124030-3 s 4\p DE-604 https://doi.org/10.1007/978-3-642-65567-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bognár, János Indefinite Inner Product Spaces Mathematics Mathematics, general Mathematik Funktionalanalysis (DE-588)4018916-8 gnd Indefinites Skalarprodukt (DE-588)4161471-9 gnd Raum Mathematik (DE-588)4124030-3 gnd Produktraum (DE-588)4130367-2 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4161471-9 (DE-588)4124030-3 (DE-588)4130367-2 |
| title | Indefinite Inner Product Spaces |
| title_auth | Indefinite Inner Product Spaces |
| title_exact_search | Indefinite Inner Product Spaces |
| title_full | Indefinite Inner Product Spaces by János Bognár |
| title_fullStr | Indefinite Inner Product Spaces by János Bognár |
| title_full_unstemmed | Indefinite Inner Product Spaces by János Bognár |
| title_short | Indefinite Inner Product Spaces |
| title_sort | indefinite inner product spaces |
| topic | Mathematics Mathematics, general Mathematik Funktionalanalysis (DE-588)4018916-8 gnd Indefinites Skalarprodukt (DE-588)4161471-9 gnd Raum Mathematik (DE-588)4124030-3 gnd Produktraum (DE-588)4130367-2 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Funktionalanalysis Indefinites Skalarprodukt Raum Mathematik Produktraum |
| url | https://doi.org/10.1007/978-3-642-65567-8 |
| work_keys_str_mv | AT bognarjanos indefiniteinnerproductspaces |