Spinors in Hilbert Space:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
1974
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 1. Hilbert Space The words "Hilbert space" here will always denote what mathematicians call a separable Hilbert space. It is composed of vectors each with a denumerable infinity of coordinates ql' q2' Q3, .... Usually the coordinates are considered to be complex numbers and each vector has a squared length ~rIQrI2. This squared length must converge in order that the q's may specify a Hilbert vector. Let us express qr in terms of real and imaginary parts, qr = Xr + iYr' Then the squared length is l:.r(x; + y;). The x's and y's may be looked upon as the coordinates of a vector. It is again a Hilbert vector, but it is a real Hilbert vector, with only real coordinates. Thus a complex Hilbert vector uniquely determines a real Hilbert vector. The second vector has, at first sight, twice as many coordinates as the first one. But twice a denumerable infinity is again a denumerable infinity, so the second vector has the same number of coordinates as the first. Thus a complex Hilbert vector is not a more general kind of quantity than a real one |
| Beschreibung: | 1 Online-Ressource (VII, 91 p) |
| ISBN: | 9781475700343 9781475700367 |
| DOI: | 10.1007/978-1-4757-0034-3 |
Internformat
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| 245 | 1 | 0 | |a Spinors in Hilbert Space |c by P. A. M. Dirac |
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| 500 | |a 1. Hilbert Space The words "Hilbert space" here will always denote what mathematicians call a separable Hilbert space. It is composed of vectors each with a denumerable infinity of coordinates ql' q2' Q3, .... Usually the coordinates are considered to be complex numbers and each vector has a squared length ~rIQrI2. This squared length must converge in order that the q's may specify a Hilbert vector. Let us express qr in terms of real and imaginary parts, qr = Xr + iYr' Then the squared length is l:.r(x; + y;). The x's and y's may be looked upon as the coordinates of a vector. It is again a Hilbert vector, but it is a real Hilbert vector, with only real coordinates. Thus a complex Hilbert vector uniquely determines a real Hilbert vector. The second vector has, at first sight, twice as many coordinates as the first one. But twice a denumerable infinity is again a denumerable infinity, so the second vector has the same number of coordinates as the first. Thus a complex Hilbert vector is not a more general kind of quantity than a real one | ||
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Datensatz im Suchindex
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| author | Dirac, P. A. M. |
| author_facet | Dirac, P. A. M. |
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| dewey-full | 530.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1 |
| dewey-search | 530.1 |
| dewey-sort | 3530.1 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| doi_str_mv | 10.1007/978-1-4757-0034-3 |
| format | Electronic eBook |
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| id | DE-604.BV042412233 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:20:50Z |
| institution | BVB |
| isbn | 9781475700343 9781475700367 |
| language | English |
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| physical | 1 Online-Ressource (VII, 91 p) |
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| spelling | Dirac, P. A. M. Verfasser aut Spinors in Hilbert Space by P. A. M. Dirac Boston, MA Springer US 1974 1 Online-Ressource (VII, 91 p) txt rdacontent c rdamedia cr rdacarrier 1. Hilbert Space The words "Hilbert space" here will always denote what mathematicians call a separable Hilbert space. It is composed of vectors each with a denumerable infinity of coordinates ql' q2' Q3, .... Usually the coordinates are considered to be complex numbers and each vector has a squared length ~rIQrI2. This squared length must converge in order that the q's may specify a Hilbert vector. Let us express qr in terms of real and imaginary parts, qr = Xr + iYr' Then the squared length is l:.r(x; + y;). The x's and y's may be looked upon as the coordinates of a vector. It is again a Hilbert vector, but it is a real Hilbert vector, with only real coordinates. Thus a complex Hilbert vector uniquely determines a real Hilbert vector. The second vector has, at first sight, twice as many coordinates as the first one. But twice a denumerable infinity is again a denumerable infinity, so the second vector has the same number of coordinates as the first. Thus a complex Hilbert vector is not a more general kind of quantity than a real one Physics Theoretical, Mathematical and Computational Physics Spinor (DE-588)4182327-8 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Spinoranalysis (DE-588)4182329-1 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 s Spinor (DE-588)4182327-8 s 1\p DE-604 Spinoranalysis (DE-588)4182329-1 s 2\p DE-604 https://doi.org/10.1007/978-1-4757-0034-3 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 |
| spellingShingle | Dirac, P. A. M. Spinors in Hilbert Space Physics Theoretical, Mathematical and Computational Physics Spinor (DE-588)4182327-8 gnd Hilbert-Raum (DE-588)4159850-7 gnd Spinoranalysis (DE-588)4182329-1 gnd |
| subject_GND | (DE-588)4182327-8 (DE-588)4159850-7 (DE-588)4182329-1 |
| title | Spinors in Hilbert Space |
| title_auth | Spinors in Hilbert Space |
| title_exact_search | Spinors in Hilbert Space |
| title_full | Spinors in Hilbert Space by P. A. M. Dirac |
| title_fullStr | Spinors in Hilbert Space by P. A. M. Dirac |
| title_full_unstemmed | Spinors in Hilbert Space by P. A. M. Dirac |
| title_short | Spinors in Hilbert Space |
| title_sort | spinors in hilbert space |
| topic | Physics Theoretical, Mathematical and Computational Physics Spinor (DE-588)4182327-8 gnd Hilbert-Raum (DE-588)4159850-7 gnd Spinoranalysis (DE-588)4182329-1 gnd |
| topic_facet | Physics Theoretical, Mathematical and Computational Physics Spinor Hilbert-Raum Spinoranalysis |
| url | https://doi.org/10.1007/978-1-4757-0034-3 |
| work_keys_str_mv | AT diracpam spinorsinhilbertspace |