Noncommutative spacetimes: symmetries in noncommutative geometry and field theory
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Dordrecht [u. a.]
Springer
2009
|
| Series: | Lecture notes in physics
774 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 199 S. 24 cm |
| ISBN: | 3540897925 9783540897927 9783540897934 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804139926287024128 |
|---|---|
| adam_text | CONTENTS PART I DEFORMED FIELD THEORY: PHYSICAL ASPECTS 1 DIFFERENTIAL
CALCULUS AND GAUGE TRANSFORMATIONS ON A DEFORMED SPACE 3 JULIUS WESS 1.1
INTRODUCTION 3 1.2 THE ALGEBRA 5 1.3 THE STAR PRODUCT 8 1.4 A DEFORMED
DIFFERENTIAL CALCULUS 10 1.5 A DEFORMED ALGEBRA OF DIFFERENTIAL
OPERATORS 11 1.6 GAUGE TRANSFORMATIONS 13 1.7 DIFFEOMORPHISM 16 1.8
CONCLUSION 17 1.9 APPENDIX 17 REFERENCES , 20 2 DEFORMED GAUGE THEORIES
23 JULIUS WESS 2.1 INTRODUCTION 23 2.2 GAUGE TRANSFORMATIONS 24 2.3 HOPF
ALGEBRA TECHNIQUES 26 2.4 FIELD EQUATIONS 27 2.5 MATTER FIELDS 30 2.6
EXAMPLES 31 REFERENCES 36 3 EINSTEIN GRAVITY ON DEFORMED SPACES 39
JULIUS WESS 3.1 INTRODUCTION 39 3.2 DIFFERENTIAL OPERATORS 40 3.3 TENSOR
FIELDS 43 3.4 EINSTEIN-HILBERT GRAVITY 46 REFERENCES 51 XI
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/991010779 DIGITALISIERT
DURCH XII CONTENTS 4 DEFORMED GAUGE THEORY: TWIST VERSUS SEIBERG-WITTEN
APPROACH . . 53 MARIJA DIMITRIJEVIC 4.1 INTRODUCTION 53 4.2 0-DEFORMED
SPACE 54 4.3 TWISTED GAUGE THEORY 59 4.3.1 GAUGE TRANSFORMATIONS 59
4.3.2 FIELD STRENGTH TENSOR 61 4.3.3 EQUATIONS OF MOTION 62 4.4
SEIBERG-WITTEN GAUGE THEORY 64 4.4.1 ENVELOPING ALGEBRA APPROACH 65
4.4.2 SEIBERG-WITTEN MAP 66 4.5 COMMENTS 69 REFERENCES 70 5 ANOTHER
EXAMPLE OF NONCOMMUTATIVE SPACES: IC-DEFORMED SPACE ... 73 MARIJA
DIMITRIJEVIC 5.1 INTRODUCTION 73 5.2 JC-DEFORMED SPACE 74 5.3 STAR
PRODUCT APPROACH 78 5.4 GAUGE THEORY ON THE K-DEFORMED SPACE 79 5.5
GAUGE FIELDS 81 5.6 INTEGRAL AND THE ACTION 82 REFERENCES 84 PART II
NONCOMMUTATIVE GEOMETRIES: FOUNDATIONS AND APPLICATIONS 6 NONCOMMUTATIVE
SPACES 89 FEDELE LIZZI 6.1 COMMUTATIVE GEOMETRY (AND TOPOLOGY) 89 6.1.1
TOPOLOGY AND ALGEBRAS 90 6.1.2 RECONSTRUCTING THE SPACE FROM THE ALGEBRA
92 6.1.3 GEOMETRICAL STRUCTURES 94 6.2 NONCOMMUTATIVE SPACES 95 6.2.1
THE GNS CONSTRUCTION 96 6.2.2 COMMUTATIVE AND NONCOMMUTATIVE SPACES 99
6.2.3 DEFORMATIONS OF SPACES 100 6.3 THE NONCOMMUTATIVE GEOMETRY OF
CANONICAL COMMUTATION RELATIONS 101 6.4 FINAL REMARKS 108 REFERENCES 108
7 QUANTUM GROUPS, QUANTUM LIE ALGEBRAS AND TWISTS IL CONTENTS XIII 7.5
DUALITY 119 7.6 QUANTUM LIE ALGEBRA 122 7.7 DEFORMATION BY TWIST AND
QUANTUM POINCARE LIE ALGEBRA 124 APPENDIX 127 7.8 ALGEBRAS, COALGEBRAS,
AND HOPF ALGEBRAS 127 7.9 HOPF ALGEBRA TWISTS 130 REFERENCES 131 8
NONCOMMUTATIVE SYMMETRIES AND GRAVITY 133 PAOLO ASCHIERI 8.1
INTRODUCTION 133 8.2 DEFORMATION BY TWISTS 135 8.2.1 THE TWIST & 136
8.2.2 *-TENSOR ALGEBRA 139 8.2.3 *-DIFFEOMORPHISM SYMMETRY 143 8.2.3.1
RELATION BETWEEN C/S* AND UE^ 149 8.2.4 TWISTED VERSUS SPONTANEOUSLY
BROKEN SYMMETRIES 150 8.3 POINCARE SYMMETRY 152 8.3.1 *-POINCARE ALGEBRA
152 8.3.2 TWISTED POINCARE ALGEBRA 155 8.4 COVARIANT DERIVATIVE,
TORSION, AND CURVATURE 156 8.5 METRIC AND EINSTEIN EQUATIONS 158
APPENDIX 159 8.6 DIFFERENTIAL OPERATORS AND VECTOR FIELDS 159 8.7 PROOF
THAT THE COPRODUCT A+ IS COASSOCIATIVE 161 8.8 PROOF THAT THE BRACKET U
V]* IS THE ADJOINT ACTION 162 REFERENCES 162 9 TWIST DEFORMATIONS OF
QUANTUM INTEGRABLE SPIN CHAINS 165 PETR KULISH 9.1 INTRODUCTION 165 9.2
ALGEBRAIC BETHE ANSATZ (QISM) 170 9.2.1 QISM FOR THE XXX MODEL 171
9.2.1.1 THE YANGIAN ^(S/(2)) 175 9.2.1. XIV CONTENTS 10 THE
NONCOMMUTATIVE GEOMETRY OF JULIUS WESS 189 PAOLO ASCHIERI REFERENCES 193
INDEX 197
|
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| id | DE-604.BV035717143 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:51:50Z |
| institution | BVB |
| isbn | 3540897925 9783540897927 9783540897934 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017993983 |
| oclc_num | 430520254 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-11 |
| owner_facet | DE-384 DE-703 DE-11 |
| physical | XIV, 199 S. 24 cm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in physics |
| series2 | Lecture notes in physics |
| spelling | Noncommutative spacetimes symmetries in noncommutative geometry and field theory P. Aschieri ... Dordrecht [u. a.] Springer 2009 XIV, 199 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 774 Feldtheorie (DE-588)4016698-3 gnd rswk-swf Nichtkommutative Geometrie (DE-588)4171742-9 gnd rswk-swf Feldtheorie (DE-588)4016698-3 s Nichtkommutative Geometrie (DE-588)4171742-9 s DE-604 Aschieri, Paolo Sonstige oth Lecture notes in physics 774 (DE-604)BV000003166 774 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017993983&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Noncommutative spacetimes symmetries in noncommutative geometry and field theory Lecture notes in physics Feldtheorie (DE-588)4016698-3 gnd Nichtkommutative Geometrie (DE-588)4171742-9 gnd |
| subject_GND | (DE-588)4016698-3 (DE-588)4171742-9 |
| title | Noncommutative spacetimes symmetries in noncommutative geometry and field theory |
| title_auth | Noncommutative spacetimes symmetries in noncommutative geometry and field theory |
| title_exact_search | Noncommutative spacetimes symmetries in noncommutative geometry and field theory |
| title_full | Noncommutative spacetimes symmetries in noncommutative geometry and field theory P. Aschieri ... |
| title_fullStr | Noncommutative spacetimes symmetries in noncommutative geometry and field theory P. Aschieri ... |
| title_full_unstemmed | Noncommutative spacetimes symmetries in noncommutative geometry and field theory P. Aschieri ... |
| title_short | Noncommutative spacetimes |
| title_sort | noncommutative spacetimes symmetries in noncommutative geometry and field theory |
| title_sub | symmetries in noncommutative geometry and field theory |
| topic | Feldtheorie (DE-588)4016698-3 gnd Nichtkommutative Geometrie (DE-588)4171742-9 gnd |
| topic_facet | Feldtheorie Nichtkommutative Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017993983&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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