Spin representations of the q-Poincaré algebra:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English German |
| Veröffentlicht: |
2001
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | München, Univ., Fak. für Physik, Diss., 2001 |
| Beschreibung: | 99 S. |
Internformat
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Datensatz im Suchindex
| _version_ | 1812460690861981696 |
|---|---|
| adam_text |
CONTENTS
INTRODUCTION 6
1 CONSTRUCTION OF THE G-LORENTZ ALGEBRA 10
1.1 ^-SPINORS AND
SUQ(2). 11
1.1.1 9-SPINORS AND THEIR COTRANSFORMATIONS. 11
1.1.2 THE 9-SPINOR METRIC AND SLG(2). 12
1.1.3 UPPER SPINOR INDICES, CONJUGATION, AND SUQ(2) . 12
1.2 THE 9-LORENTZ GROUP. 13
1.2.1 DOTTED SPINORS. 13
1.2.2 COMMUTATION RELATIONS OF THE 9-LORENTZ GROUP. 14
1.3 THE 9-LORENTZ ALGEBRA AS DUAL OF THE 9-LORENTZ GROUP . 15
1.3.1 UQ(S\I
2
) AS DUAL OF SUQ{2). 16
1.3.2 COMPUTING THE DUAL OF THE 9-LORENTZ GROUP. 17
2 STRUCTURE OF THE G-LORENTZ ALGEBRA 20
2.1 REPRESENTATION THEORY OF THE 9-LORENTZ ALGEBRA. 20
2.1.1 THE CLEBSCH-GORDAN SERIES OF WG(SL2). 20
2.1.2 CLEBSCH-GORDAN COEFFICIENTS OF THE 9-LORENTZ ALGEBRA . 21
2.2 TENSOR OPERATORS. 22
2.2.1 TENSOR OPERATORS IN HOPF ALGEBRAS. 22
2.2.2 TENSOR OPERATORS OF
W9(SU2)
. 24
2.2.3 THE VECTOR FORM OF T/G(SU2). 25
2.3 THE 9-LORENTZ ALGEBRA AS QUANTUM DOUBLE . 27
2.3.1 ROTATIONS AND THE SUG(2)OP ALGEBRA OF BOOSTS. 27
2.3.2 L-MATRICES AND THE EXPLICIT FORM OF THE BOOST ALGEBRA . . 29
2.3.3 COMMUTATION RELATIONS BETWEEN BOOSTS AND ROTATIONS . . 30
2.4 THE VECTORIAL FORM OF THE 9-LORENTZ ALGEBRA. 62
2.4.1 TENSOR OPERATORS OF THE 9-LORENTZ ALGEBRA. 32
2.4.2 THE VECTORIAL GENERATORS. 33
2.4.3 RELATIONS WITH THE OTHER GENERATORS. 34
3 ALGEBRAIC STRUCTURE OF THE G-POINCARE ALGEBRA 36
3.1 THE 9-POINCARE ALGEBRA. 36
3.1.1 CONSTRUCTION OF THE 9-MINKOWSKI-SPACE ALGEBRA. 36
3.1.2 4-VECTORS AND THE 9-PAULI MATRICES. 37
3.1.3 COMMUTATION RELATIONS OF THE 9-POINCARE ALGEBRA. 40
3.2 THE 9-PAULI-LUBANSKI VECTOR AND THE SPIN CASIMIR. 42
3.2.1 THE 9-EUCLIDEAN ALGEBRA. 42
3.2.2 THE CENTER OF THE 9-EUCLIDEAN ALGEBRA. 44
3.2.3 THE PAULI-LUBANSKI VECTOR IN THE 9-DEFORMED SETTING . 45
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/962986674
CONTENTS
5
3.2.4 BOOSTING THE G-PAULI-LUBANSKI VECTOR. 46
3.3 THE LITTLE ALGEBRAS. 51
3.3.1 LITTLE ALGEBRAS IN THE G-DEFORMED SETTING . 51
3.3.2 COMPUTATION OF THE G-LITTLE ALGEBRAS. 53
4 MASSIVE SPIN REPRESENTATIONS 55
4.1 REPRESENTATIONS IN AN ANGULAR MOMENTUM BASIS. 55
4.1.1 THE COMPLETE SET OF COMMUTING OBSERVABLES. 55
4.1.2 REPRESENTATIONS OF THE G-EUCLIDEAN ALGEBRA. 57
4.1.3 POSSIBLE TRANSITIONS OF ENERGY AND HELICITY. 58
4.1.4 DEPENDENCE ON TOTAL ANGULAR MOMENTUM. 59
4.1.5 DEPENDENCE ON THE OTHER QUANTUM NUMBERS. 61
4.2 REPRESENTATIONS BY INDUCTION . 66
4.2.1 THE METHOD OF INDUCED REPRESENTATIONS OF ALGEBRAS . 66
4.2.2 INDUCED REPRESENTATIONS OF THE G-POINEARE ALGEBRA . 67
5 FREE WAVE EQUATIONS 69
5.1 GENERAL WAVE EQUATIONS. 69
5.1.1 WAVE EQUATIONS BY REPRESENTATION THEORY. 69
5.1.2 G-LORENTZ SPINORS. 70
5.1.3 CONJUGATE SPINORS . 72
5.2 THE G-DIRAC EQUATION. 74
5.2.1 THE G-DIRAC EQUATION IN THE REST FRAME. 74
5.2.2 THE G-GAMMA MATRICES AND THE G-CLIFFORD ALGEBRA . 75
5.2.3 THE ZERO MASS LIMIT AND THE G-WEYL EQUATIONS. 77
5.3 THE G-MAXWELL EQUATIONS . 78
5.3.1 THE G-MAXWELL EQUATIONS IN THE MOMENTUM EIGENSPACES . 78
5.3.2 COMPUTING THE G-MAXWELL EQUATION. 79
5.3.3 THE G-ELECTROMAGNETIC FIELD. 82
A USEFUL FORMULAS 84
A.L CLEBSCH-GORDAN COEFFICIENTS. 84
A. 1.1 CLEBSCH-GORDAN AND RACAH COEFFICIENTS FOR UQ{SU2) . 84
A.L.2 METRIC AND EPSILON TENSOR. 85
A.1.3 CLEBSCH-GORDAN COEFFICIENTS FOR THE G-LORENTZ ALGEBRA . . 88
A.2 REPRESENTATIONS. 90
A.2.1 REPRESENTATIONS OF (SU2). 90
A.2.2 REPRESENTATIONS OF THE G-LORENTZ ALGEBRA. 91
A.3 77-MATRICES. 92
A.3.1 THE 77-MATRIX OF UQ(SU2). 93
A.3.2 THE 77-MATRICES OF THE G-LORENTZ ALGEBRA. 94
BIBLIOGRAPHY
95 |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV013962633 |
| illustrated | Not Illustrated |
| indexdate | 2024-10-09T18:06:47Z |
| institution | BVB |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009555874 |
| oclc_num | 248367480 |
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| owner_facet | DE-19 DE-BY-UBM DE-12 |
| physical | 99 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
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| spelling | Blohmann, Christian 1971- Verfasser (DE-588)123300568 aut Spin representations of the q-Poincaré algebra von Christian Blohmann 2001 99 S. txt rdacontent n rdamedia nc rdacarrier München, Univ., Fak. für Physik, Diss., 2001 Inhomogene Lorentz-Gruppe - Quantengruppe - Spin - Irreduzible Darstellung Spin (DE-588)4125988-9 gnd rswk-swf Inhomogene Lorentz-Gruppe (DE-588)4359420-7 gnd rswk-swf Irreduzible Darstellung (DE-588)4162430-0 gnd rswk-swf Quantengruppe (DE-588)4252437-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Inhomogene Lorentz-Gruppe (DE-588)4359420-7 s Quantengruppe (DE-588)4252437-4 s Spin (DE-588)4125988-9 s Irreduzible Darstellung (DE-588)4162430-0 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009555874&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blohmann, Christian 1971- Spin representations of the q-Poincaré algebra Inhomogene Lorentz-Gruppe - Quantengruppe - Spin - Irreduzible Darstellung Spin (DE-588)4125988-9 gnd Inhomogene Lorentz-Gruppe (DE-588)4359420-7 gnd Irreduzible Darstellung (DE-588)4162430-0 gnd Quantengruppe (DE-588)4252437-4 gnd |
| subject_GND | (DE-588)4125988-9 (DE-588)4359420-7 (DE-588)4162430-0 (DE-588)4252437-4 (DE-588)4113937-9 |
| title | Spin representations of the q-Poincaré algebra |
| title_auth | Spin representations of the q-Poincaré algebra |
| title_exact_search | Spin representations of the q-Poincaré algebra |
| title_full | Spin representations of the q-Poincaré algebra von Christian Blohmann |
| title_fullStr | Spin representations of the q-Poincaré algebra von Christian Blohmann |
| title_full_unstemmed | Spin representations of the q-Poincaré algebra von Christian Blohmann |
| title_short | Spin representations of the q-Poincaré algebra |
| title_sort | spin representations of the q poincare algebra |
| topic | Inhomogene Lorentz-Gruppe - Quantengruppe - Spin - Irreduzible Darstellung Spin (DE-588)4125988-9 gnd Inhomogene Lorentz-Gruppe (DE-588)4359420-7 gnd Irreduzible Darstellung (DE-588)4162430-0 gnd Quantengruppe (DE-588)4252437-4 gnd |
| topic_facet | Inhomogene Lorentz-Gruppe - Quantengruppe - Spin - Irreduzible Darstellung Spin Inhomogene Lorentz-Gruppe Irreduzible Darstellung Quantengruppe Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009555874&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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