The Schrödinger-Virasoro algebra: mathematical structure and dynamical Schrödinger symmetries
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
2012
|
| Schriftenreihe: | Theoretical and mathematical physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XLII, 302 S. graph. Darst. 25 cm |
| ISBN: | 9783642227165 3642227163 9783642227172 |
Internformat
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| 100 | 1 | |a Unterberger, Jérémie |d 1974- |e Verfasser |0 (DE-588)101923640X |4 aut | |
| 245 | 1 | 0 | |a The Schrödinger-Virasoro algebra |b mathematical structure and dynamical Schrödinger symmetries |c Jérémie Unterberger ; Claude Roger |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c 2012 | |
| 300 | |a XLII, 302 S. |b graph. Darst. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Theoretical and mathematical physics | |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Roger, Claude |d 1949- |e Verfasser |0 (DE-588)1019139900 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1805145937065017344 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
FOREWORD (BY MALTE HENKEL) V
PREFACE XXIII
1 GEOMETRIE DEFINITIONS OF SO 1
1.1 FROM NEWTONIAN MECHANICS TO THE SCHROEDINGER- VIRASORO ALGEBRA 1
1.1.1 FROM GALILEI TO SCHROEDINGER: CENTRAL EXTENSIONS AND PROJECTIVE
AUTOMORPHISMS 3
1.1.2 FROM SCHROEDINGER TO SCHROEDINGER-VIRASORO 7
1.1.3 OUR OBJECT OF STUDY: THE SCHROEDINGER- VIRASORO ALGEBRA IN ONE
SPACE DIMENSION 11
1.2 INTEGRATION OF THE SCHROEDINGER-VIRASORO ALGEBRA TO A GROUP 12
2 BASIC ALGEBRAIC AND GEOMETRIC FEATURES 17
2.1 ON GRADUATIONS AND SOME DEFORMATIONS OF THE LIE ALGEBRA SO 18
2.2 THE CONFORMAI EMBEDDING 20
2.3 RELATIONS BETWEEN SO AND THE POISSON ALGEBRA ON T*S L AND
'NO-GO'THEOREM 23
2.4 CONFORMAI AND SCHROEDINGER TENSOR INVARIANTS 27
3 COADJOINT REPRESENTATION OF THE SCHROEDINGER-VIRASORO GROUP 31 3.1
COADJOINT ACTION OF SO 32
3.2 COADJOINT ORBITS OF SO 37
4 INDUCED REPRESENTATIONS AND VERMA MODULES 43
4.1 INTRODUCTION AND NOTATIONS 43
4.2 KAC DETERMINANT FORMULA FOR VECT(5') X SS'O 46
4.3 KAC DETERMINANT FORMULA FOR SO 52
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1012996344
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
COINDUCED REPRESENTATIONS 57
5.1 THE LIE ALGEBRA SO AS A CARTAN PROLONGATION 58
5.2 ABOUT MULTI-DIAGONAL DIFFERENTIAL OPERATORS AND SOME
VIRASORO-SOLVABLE LIE ALGEBRAS 61
5.3 COINDUCED REPRESENTATIONS OF SO 68
5.4 EXAMPLES OF COINDUCED REPRESENTATIONS 72
VERTEX REPRESENTATIONS 75
6.1 ON THE EXTENDED SCHROEDINGER-VIRASORO LIE ALGEBRA S~B AND ITS
COINDUCED REPRESENTATIONS 77
6.2 THE SCHROEDINGER-VIRASORO PRIMARY FIELDS AND THE SUPERFIELD
INTERPRETATION OF SO 81
6.2.1 DEFINITION OF THE SCHROEDINGER-VIRASORO PRIMARY FIELDS 82
6.2.2 A SUPERFIELD INTERPRETATION 86
6.3 CONSTRUCTION BY F/( 1 )-CURRENTS OR A-THEORY 89
6.3.1 DEFINITION OF THE SO-FIELDS 89
6.3.2 CONSTRUCTION OF THE GENERALIZED POLYNOMIAL FIELDS *I;,* 95
6.4 CORRELATORS OF THE POLYNOMIAL AND GENERALIZED POLYNOMIAL FIELDS 106
6.5 CONSTRUCTION OF THE MASSIVE FIELDS I LL
COHOMOLOGY, EXTENSIONS AND DEFORMATIONS 125
7.1 SOME PREREQUISITES ABOUT LIE ALGEBRA COHOMOLOGY 126 7.2 CLASSIFYING
DEFORMATIONS OF SO(O) 128
7.3 COMPUTATION OF// 2 (SO (O),R) 138
7.4 ABOUT DEFORMATIONS OF SO I(0) 141
7.5 COMING BACK TO THE ORIGINAL SCHROEDINGER-VIRASORO ALGEBRA . 144
ACTION OF SO ON SCHROEDINGER AND DIRAC OPERATORS 147
8.1 DEFINITIONS AND NOTATIONS 148
8.2 AFFINE SCHROEDINGER COCYCLES 154
8.3 ACTION ON DIRAC-LEVY-LEBLOND OPERATORS 157
MONODROMY OF SCHROEDINGER OPERATORS 161
9.1 INTRODUCTION 161
9.2 CLASSIFICATION OF THE SCHROEDINGER OPERATORS IN Y^/ 167
9.2.1 STATEMENT OF THE PROBLEM AND CONNECTION WITH THE CLASSIFICATION OF
HILL OPERATORS 167
9.2.2 CLASSIFICATION OF HILL OPERATORS BY THE LIFTED MONODROMY 169
9.2.3 KIRILLOV'S CLASSIFICATION OF HILL OPERATORS BY ISOTROPY SUBGROUPS
172
9.2.4 CLASSIFICATION OF THE SV-ORBITS IN S^% F 176
9.2.5 CONNECTION TO U. NIEDERER'S RESULTS 181
IMAGE 3
CONTENTS
9.3 MONODROMY OF TIME-DEPENDENT SCHROEDINGER OPERATORS OF NON-RESONANT
TYPES AND ERMAKOV-LEWIS INVARIANTS 182
9.3.1 ERMAKOV-LEWIS INVARIANTS AND SCHROEDINGER- VIRASORO INVARIANCE 182
9.3.2 SOLUTION OF THE ASSOCIATED CLASSICAL PROBLEM 189 9.3.3 SPECTRAL
DECOMPOSITION OF THE MODEL OPERATORS 191 9.3.4 MONODROMY OF NON-RESONANT
HARMONIC OSCILLATORS (ELLIPTIC CASE) 192
9.3.5 MONODROMY OF HARMONIC REPULSORS (HYPERBOLIC TYPE) 193
9.3.6 MONODROMY OF NON-RESONANT OPERATORS OF UNIPOTENT TYPE 195
9.4 SYMPLECTIC STRUCTURES AND GENERAL SOLUTION OF THE SCHROEDINGER
EQUATION 196
10 POISSON STRUCTURES AND SCHROEDINGER OPERATORS 207
10.1 INTRODUCTION 207
10.2 ALGEBRAS OF PSEUDODIFFERENTIAL SYMBOLS 210
10.3 TIME-SHIFT TRANSFORMATION AND SYMMETRIES OF THE FREE SCHROEDINGER
EQUATION 214
10.4 FROM CENTRAL COCYCLES OF {VD R ) \ TO THE KAC-MOODY ALGEBRA Q 216
10.4.1 CENTRAL COCYCLES OF ( M} R ) I 217
10.4.2 INTRODUCING THE KAC-MOODY TYPE LIE ALGEBRA G 219 10.5
CONSTRUCTION OF THE EMBEDDING/ OF (DVDC)^ INTO G 220 10.6 THE ACTION OF
SO ON SCHROEDINGER OPERATORS AS A COADJOINT ACTION 221
10.7 CONNECTION WITH THE POISSON FORMALISM 226
11 SUPERSYMMETRIC EXTENSIONS OF THE SCHROEDINGER-VIRASORO ALGEBRA 23 1
11.1 ON THE DIRAC-LEVY-LEBLOND EQUATION 233
11.2 SUPERSYMMETRY IN THREE DIMENSIONS AND SUPERSYMMETRIC
SCHROEDINGER-INVARIANCE 240
11.2.1 FROM N = 2 SUPERSYMMETRY TO THE SUPER- SCHROEDINGER EQUATION 240
11.2.2 DYNAMIC SYMMETRIES OF THE SUPER- SCHROEDINGER MODEL 245
11.2.3 SOME PHYSICAL APPLICATIONS 248
11.2.4 DYNAMIC SYMMETRIES OF THE (3|2)- SUPERSYMMETRIC MODEL 249
11.2.5 FIRST CORRESPONDENCE WITH POISSON STRUCTURES: THE
SUPER-SCHROEDINGER MODEL 250
IMAGE 4
CONTENTS
11.2.6 SECOND CORRESPONDENCE WITH POISSON STRUCTURES: THE CASE OF
OSP(2|4), OR THE (3|2)-SUPERSYMMETRIC MODEL 254
11.3 EXTENDED SUPER-SCHROEDINGER TRANSFORMATIONS 257
11.3.1 ELEMENTARY EXAMPLES 258
11.3.2 GENERAL CASE 260
11.3.3 STUDY OF THE CASE N =2 264
11.4 TWO-POINT FUNCTIONS 267
A APPENDIX TO CHAPTER 6 273
B APPENDIX TO CHAPTER 11 281
B.I SUPERSYMMETRIC TWO-POINT FUNCTIONS 281
B.I.I S (1) -COVARIANT TWO-POINT FUNCTIONS 281
B. 1.2 S 2) -COVARIANT TWO-POINT FUNCTIONS 284
B.I .3 OSP(2|2)-COVARIANT TWO-POINT FUNCTIONS 284
B.1.4 SE(3|2)-COVARIANT TWO-POINT FUNCTIONS 288
B.I.5 OSP(2|4)-COVARIANT TWO-POINT FUNCTIONS 289
B.2 TABLE OF LIE SUPERALGEBRAS 289
REFERENCES 293
INDEX 299 |
| any_adam_object | 1 |
| author | Unterberger, Jérémie 1974- Roger, Claude 1949- |
| author_GND | (DE-588)101923640X (DE-588)1019139900 |
| author_facet | Unterberger, Jérémie 1974- Roger, Claude 1949- |
| author_role | aut aut |
| author_sort | Unterberger, Jérémie 1974- |
| author_variant | j u ju c r cr |
| building | Verbundindex |
| bvnumber | BV039837630 |
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| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
| dewey-search | 530.12 |
| dewey-sort | 3530.12 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV039837630 |
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| indexdate | 2024-07-21T00:21:57Z |
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| language | English |
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| spelling | Unterberger, Jérémie 1974- Verfasser (DE-588)101923640X aut The Schrödinger-Virasoro algebra mathematical structure and dynamical Schrödinger symmetries Jérémie Unterberger ; Claude Roger Berlin ; Heidelberg Springer 2012 XLII, 302 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Theoretical and mathematical physics Literaturangaben Schrödinger-Virasoro-Algebra (DE-588)7843879-2 gnd rswk-swf Schrödinger-Virasoro-Algebra (DE-588)7843879-2 s DE-604 Roger, Claude 1949- Verfasser (DE-588)1019139900 aut Erscheint auch als Online-Ausgabe The Schrödinger-Virasoro Algebra X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3845092&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024697589&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Unterberger, Jérémie 1974- Roger, Claude 1949- The Schrödinger-Virasoro algebra mathematical structure and dynamical Schrödinger symmetries Schrödinger-Virasoro-Algebra (DE-588)7843879-2 gnd |
| subject_GND | (DE-588)7843879-2 |
| title | The Schrödinger-Virasoro algebra mathematical structure and dynamical Schrödinger symmetries |
| title_auth | The Schrödinger-Virasoro algebra mathematical structure and dynamical Schrödinger symmetries |
| title_exact_search | The Schrödinger-Virasoro algebra mathematical structure and dynamical Schrödinger symmetries |
| title_full | The Schrödinger-Virasoro algebra mathematical structure and dynamical Schrödinger symmetries Jérémie Unterberger ; Claude Roger |
| title_fullStr | The Schrödinger-Virasoro algebra mathematical structure and dynamical Schrödinger symmetries Jérémie Unterberger ; Claude Roger |
| title_full_unstemmed | The Schrödinger-Virasoro algebra mathematical structure and dynamical Schrödinger symmetries Jérémie Unterberger ; Claude Roger |
| title_short | The Schrödinger-Virasoro algebra |
| title_sort | the schrodinger virasoro algebra mathematical structure and dynamical schrodinger symmetries |
| title_sub | mathematical structure and dynamical Schrödinger symmetries |
| topic | Schrödinger-Virasoro-Algebra (DE-588)7843879-2 gnd |
| topic_facet | Schrödinger-Virasoro-Algebra |
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