Irreducible Cartesian tensors:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2018]
|
| Schriftenreihe: | De Gruyter studies in mathematical physics
volume 43 |
| Schlagworte: | |
| Online-Zugang: | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110563634&searchTitles=true Inhaltsverzeichnis |
| Beschreibung: | X, 255 Seiten 12 Illustrationen 24 cm x 17 cm |
| ISBN: | 9783110563634 3110563630 |
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| 245 | 1 | 0 | |a Irreducible Cartesian tensors |c Robert F. Snider |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2018] | |
| 264 | 4 | |c © 2018 | |
| 300 | |a X, 255 Seiten |b 12 Illustrationen |c 24 cm x 17 cm | ||
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Datensatz im Suchindex
| _version_ | 1804178134676799488 |
|---|---|
| adam_text | CONTENTS
PREFACE* V
LIST OF FIGURES* XI
1 INTRODUCTION * 1
2 VECTORIAL APPROACH * 9
2.1 AN INTRODUCTION TO VECTORS AND TENSORS * 9
2.2 THE FOUR ELEMENTARY TENSOR OPERATIONS * 13
2.3 ROTATIONS IN TWO DIMENSIONS * 15
2.3.1 ROTATION BY 7
T
/2 * 16
2.3.2 TENSORIAL DESCRIPTION OF A ROTATION * 17
2.3.3 GROUP THEORY ASPECTS * 18
2.4 DIAGRAMMATIC REPRESENTATION OF TENSORS * 21
2.5 ROTATIONS IN THREE DIMENSIONS * 26
2.5.1 THE 3-DIMENSIONAL ROTATION GROUP * 29
2.5.2 EULERIAN ANGLES * 32
2.5.3 PASSIVE ROTATIONS * 37
3 TENSORS AND THEIR ROTATIONAL REDUCTION * 41
3.1 THE ROTATIONAL INVARIANCE OF U AND E * 45
3.2 INVARIANT EMBEDDING AND TENSORIAL REDUCTION * 47
3.2.1 INVARIANT EMBEDDING * 47
3.2.2 REDUCTION AND NATURAL TENSORS * 48
3.3 THE NATURAL PROJECTION TENSORS * 51
3.3.1 CONTRACTION OF E ^ * 53
3.3.2 SELECTION OF A DIRECTION OF E ^ * 54
3.4 NATURAL TENSORS AS IRREDUCIBLE REPRESENTATIONS * 55
3.4.1 DIMENSION OF SYMMETRIC TRACELESS TENSORS OF ORDER
P * 56
3.4.2 THE CASIMIR INVARIANT EIGENVALUE FOR A SYMMETRIC TRACELESS
TENSOR * 56
3.5 PARENTAGE SCHEME * 57
3.6 METHOD OF CHARACTERS * 59
3.6.1 GROUP DENSITY * 59
3.6.2 CLASSIFICATION OF TENSORS OF ORDERPVIA CHARACTERS * 61
4 TENSORS OF R * 67
4.1 NATURAL TENSORS OF R * 67
4.2 INTEGRALS OF PRODUCTS O FF * 70
4.3 ORTHOGONAL FUNCTIONS OF R ASSOCIATED WITH A GAUSSIAN WEIGHT
FUNCTION
----
72
5 SPHERICAL VECTORS AND TENSORS * 75
5.1 GROUP GENERATOR PROPERTIES * 76
5.2 THE COMPONENTS OF A SPHERICAL VECTOR* 79
5.3 ROTATION OF A SPHERICAL VECTOR* 82
5.4 SPHERICAL TENSORS * 84
5.5 SPHERICAL HARMONICS * 90
6 3-J COUPLING TENSORS * 93
6.1 DEFINITIONS
----
94
6.2 DETAILED CALCULATION O F T ( L I ,L 2 ,4 ) * 96
6.2.1 T ( 4 , 4 , 4 ) FOR
L EVEN
------
96
6.2.2 THE SPECIAL CASE THAT 4 + 4 = 4 * 99
6.2.3 THE GENERAL CASE FOR
L EVEN * 100
6.2.4 T ( 4 , 4 , 4 ) F O R I ODD* 102
6.3 DETAILED CALCULATION OF 2(4,
4
,
4
)
* 104
6.3.1 2 ( 4 ,4 ,4 ) F O R I EVEN
------
105
6.3.2 2 ( 4 ,^ ,4 ) F O R I ODD
-------
107
6.4 THREE BASIC CONTRACTIONS * 108
6.5 RECURSION RELATIONS * 111
6.6 CALCULATION OF J2ABC XA,B,C * 115
6.6.1 SUM OVER
A AND B * 116
6.6.2 SUM OVER
C
----
117
6.6.3 CALCULATION OF 53AB
XA,B,O
* 117
6.6.4 J2ABC XA,B,C FOR EVEN AND ODD I * 121
7 PROPERTIES OF 3- J TENSORS * 123
7.1 COMPLETENESS RELATION * 123
7.2 INTEGRALS OVER FUNCTIONS O FF * 124
7.3 3-J SYMBOLS
----
128
7.3.1 BASIC PROPERTIES OF 3-J SYMBOLS * 129
7.4 INTEGRALS OF SPHERICAL HARMONICS * 131
7.5 INVARIANT FUNCTIONS OF THREE VECTORS * 132
7.6 CALCULATION OF TWO PARTICULAR SETS OF 3-J SYMBOLS * 137
8 THE 6-J AND OTHER
N-J SYMBOLS * 139
8.1 THE 6-J SYMBOL * 139
8.2 6-J SYMBOL PROPERTIES * 142
8.3 EVALUATION OF CERTAIN 6-J SYMBOLS * 144
8.3.1 THE CASES WHEN 1 = 0 AND 1 * 144
8.3.2 THE CASE WHEN
3
= T + * 147
8.3.3 A RECURSION RELATION * 151
8.4 THE 9-J SYMBOL
-----
152
9 ROTATION MATRICES * 155
9.1 AXIS-ANGLE REPRESENTATION * 155
9.2 EULER ANGLE REPRESENTATION * 158
9.2.1 ALTERNATE FORMULA * 159
9.3 CONNECTION WITH SPHERICAL HARMONICS * 160
9.4 PROPERTIES OF THE ROTATION MATRICES * 163
9.5 AS EIGENVECTORS OF THE ROTATION GENERATORS * 167
10 SPINORS * 169
10.1 THE STANDARD SPINOR BASIS SETS * 170
10.2 ROTATION OF A SPINOR
----
172
10.2.1 PRODUCTS OF ROTATIONS * 175
10.3 THE INVARIANT TENSOR E * 176
10.4 SPINOR INVARIANTS * 180
10.5 REDUCTION OF SPINOR TENSORS OF ORDER P * 182
10.6 SPINOR TENSORS OF WEIGHT
L * 185
10.7 3-J SPINOR TENSORS * 188
10.7.1 NORMALIZATION CALCULATION * 189
10.7.2 3-J SYMBOLS
----
191
10.8 SPINOR-CARTESIAN TRANSFORMATION * 193
10.8.1 CAYLEY-KLEIN REPRESENTATION OF A VECTOR * 196
10.9 DISCUSSION OF SPINORS * 197
11 APPLICATIONS TO QUANTUM MECHANICS * 199
11.1 EIGENVECTORS OF THE ANGULAR MOMENTUM * 200
11.1.1 ABSTRACT PROPERTIES * 201
11.1.2 POSITION REPRESENTATION * 203
11.1.3 TENSORIAL REPRESENTATION * 207
11.1.4 MOMENTUM REPRESENTATION * 207
11.2 SYMMETRIC TOP EIGENVECTORS * 209
11.2.1 ANOMALOUS COMMUTATION RELATIONS * 213
11.3 WIGNER-ECKART THEOREM * 214
11.4 TENSORS OF ANGULAR MOMENTUM * 217
11.5 TRACES OF PRODUCTS OF J * 221
11.6 ANGULAR MOMENTUM SUPEROPERATORS * 225
A SOME FORMALITIES OF LINEAR ALGEBRA * 229
A.L GROUP THEORY
-----
229
A.2 VECTOR SPACES * 234
A.3 CARTESIAN TENSORS AND POLYADICS * 242
B CALCULATION OF D $ N (0,/3,0) * 247
BIBLIOGRAPHY * 251
SYMBOL INDEX * 253
|
| any_adam_object | 1 |
| author | Snider, Robert F. |
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| author_facet | Snider, Robert F. |
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| bvnumber | BV044680096 |
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| ctrlnum | (OCoLC)1015882469 (DE-599)DNB1136878823 |
| dewey-full | 530 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530 |
| dewey-search | 530 |
| dewey-sort | 3530 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| indexdate | 2024-07-10T07:59:09Z |
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| language | English |
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| physical | X, 255 Seiten 12 Illustrationen 24 cm x 17 cm |
| publishDate | 2018 |
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| publisher | De Gruyter |
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| series | De Gruyter studies in mathematical physics |
| series2 | De Gruyter studies in mathematical physics |
| spelling | Snider, Robert F. Verfasser (DE-588)1148463542 aut Irreducible Cartesian tensors Robert F. Snider Berlin ; Boston De Gruyter [2018] © 2018 X, 255 Seiten 12 Illustrationen 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematical physics volume 43 Kartesischer Tensor (DE-588)4603780-9 gnd rswk-swf Kartesischer Tensor (DE-588)4603780-9 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-056486-0 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-056373-3 De Gruyter studies in mathematical physics volume 43 (DE-604)BV040141722 43 X:MVB http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110563634&searchTitles=true DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030077259&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Snider, Robert F. Irreducible Cartesian tensors De Gruyter studies in mathematical physics Kartesischer Tensor (DE-588)4603780-9 gnd |
| subject_GND | (DE-588)4603780-9 |
| title | Irreducible Cartesian tensors |
| title_auth | Irreducible Cartesian tensors |
| title_exact_search | Irreducible Cartesian tensors |
| title_full | Irreducible Cartesian tensors Robert F. Snider |
| title_fullStr | Irreducible Cartesian tensors Robert F. Snider |
| title_full_unstemmed | Irreducible Cartesian tensors Robert F. Snider |
| title_short | Irreducible Cartesian tensors |
| title_sort | irreducible cartesian tensors |
| topic | Kartesischer Tensor (DE-588)4603780-9 gnd |
| topic_facet | Kartesischer Tensor |
| url | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110563634&searchTitles=true http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030077259&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV040141722 |
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