Theory of group representations and applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Warszawa
Polish Scientific Publ.
1980
|
| Edition: | 2. rev. ed. |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002316289&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XIX, 717 S. |
| ISBN: | 8301027169 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1819346970143096832 |
|---|---|
| adam_text | Contents
Preface VII
Outline of the Book XV
Notations XIX
Chapter 1
Lie Algebras
§ 1. Basic Concepts and General Properties 1
§ 2. Solvable, Nilpotent, Semisimple and Simple Lie Algebras .... 10
§3. The Structure of Lie Algebras 17
§ 4. Classification of Simple, Complex Lie Algebras 20
§ 5. Classification of Simple, Real Lie Algebras 29
§ 6. The Gauss, Cartan and Iwasawa Decompositions 37
§ 7. An Application. On Unification of the Poincare Algebra and Internal
Symmetry Algebra 43
§ 8. Contraction of Lie Algebras 44
§ 9. Comments and Supplements 46
§ 10. Exercises 48
Chapter 2
Topological Groups
§ 1. Topological Spaces 52
§ 2. Topological Groups 61
§ 3. The Haar Measure 67
§ 4. Comments and Supplements 70
§ 5. Exercises 71
Chapter 3
Lie Groups
§ 1. Differentiable Manifolds 75
§ 2. Lie Groups 81
§ 3. The Lie Algebra of a Lie Group • 85
§ 4. The Direct and Semidirect Products 95
§ 5. Levi Malcev Decomposition 98
§ 6. Gauss, Cartan, Iwasawa and Bruhat Global Decompositions .... 100
§ 7. Classification of Simple Lie Groups 106
§ 8. Structure of Compact Lie Groups 108
IX
X CONTENTS
§ 9. Invariant Metric and Invariant Measure on Lie Groups 109
§ 10. Comments and Supplements Ill
§ 11. Exercises 114
Chapter 4
Homogeneous and Symmetric Spaces
§ 1. Homogeneous Spaces 123
§ 2. Symmetric Spaces 124
§ 3P Invariant and Quasi Invariant Measures on Homogeneous Spaces 128
§ 4. Comments and Supplements 132
§ 5. Exercises 132
Chapter 5
Group Representations
§ 1. Basic Concepts 134
§ 2. Equivalence of Representations 139
§ 3. Irreducibility and Reducibility 141
§ 4. Cyclic Representations 145
§ 5. Tensor Product of Representations 147
§6. Direct Integral Decomposition of Unitary Representations .... 150
§ 7. Comments and Supplements 156
§ 8. Exercises
Chapter 6
Representations of Commutative Groups
§ 1. Irreducible Representations and Characters 159
§ 2. Stone and SNAG Theorems 160
§ 3. Comments and Supplements 163
§ 4. Exercises 164
Chapter 7
Representations of Compact Groups
§ 1. Basic Properties of Representations of Compact Groups 166
§ 2. Peter Weyl and Weyl Approximation Theorems 172
§ 3. Projection Operators and Irreducible Representations 177
§ 4. Applications 179
§ 5. Representations of Finite Groups 186
§ 6. Comments and Supplements 195
§ 7. Exercises . 197
Chapter 8
Finite Dimensional Representations of Lie Groups
§ 1. General Properties of Representations of Solvable and Semisimple
Lie Groups 199
CONTENTS XI
§ 2. Induced Representations of Lie Groups 205
§ 3. The Representations of GL(n, C), GL(«, R), U(p, q), V(n), SL(n, C),
SL(n, R), SU(p, q), and SU(«) 213
§ 4. The Representations of the Symplectic Groups Sp(w, C), Sp(n, R)
and Sp(«) 217
§ 5. The Representations of Orthogonal Groups SO(«,C),SO(/7, q),SO*(n),
and SO(«) 219
§ 6. The Fundamental Representations 223
§ 7. Representations of Arbitrary Lie Groups 225
§ 8. Further Results and Comments 227
§ 9. Exercises 238
Chapter 9
Tensor Operators, Enveloping Algebras and Enveloping Fields
§ 1. The Tensor Operators 242
§ 2. The Enveloping Algebra 249
§ 3. The Invariant Operators 251
§ 4. Casimir Operators for Classical Lie Group 254
§ 5. The Enveloping Field 266
§ 6. Further Results and Comments 273
§ 7. Exercises 275
Chapter 10
The Explicit Construction of Finite Dimensional Irreducible
Representations
§ 1. The Gel fand Zetlin Method . 277
§ 2. The Tensor Method 291
§ 3. The Method of Harmonic Functions 302
.§ 4. The Method of Creation and Annihilation Operators 309
§ 5. Comments and Supplements 312
§ 6. Exercises 314
Chapter 11
Representation Theory of Lie and Enveloping Algebras by Unbounded
Operators: Analytic Vectors and Integrability
§ 1. Representations of Lie Algebras by Unbounded Operators .... 318
§ 2. Representations of Enveloping Algebras by Unbounded Operators 323
§3. Analytic Vectors and Analytic Dominance 331
§ 4. Analytic Vectors for Unitary Representations of Lie Groups .... 344
§ 5. Integrability of Representations of Lie Algebras 348
§ 6: FS3 Theory of Integrability of Lie Algebras Representations .... 352
§ 7. The Heat Equation on a Lie Group and Analytic Vectors .... 358
XII CONTENTS
§ 8. Algebraic Construction of Irreducible Representations . 365
§ 9. Comments and Supplements 372
§ 10. Exercises 373
Chapter 12
Quantum Dynamical Applications of Lie Algebra Representations
§ 1. Symmetry Algebras in Hamiltonian Formulation . 378
§ 2. Dynamical Lie Algebras 382
§ 3. Exercises 386
Chapter 13
Group Theory and Group Representations in Quantum Theory
§ 1. Group Representations in Physics 392
§ 2. Kinematical Postulates of Quantum Theory 394
§ 3. Symmetries of Physical Systems 406
§ 4. Dynamical Symmetries of Relativistic and Non Relativistic Systems 412
§ 5. Comments and Supplements 417
§ 6. Exercises 418
Chapter 14
Harmonic Analysis on Lie Groups. Special Functions and Group
Representations
§ 1. Harmonic Analysis on Abelian and Compact Lie Groups 421
§ 2. Harmonic Analysis on Unimodular Lie Groups 423
§3. Harmonic Analysis on Semidirect Product of Groups 431
§ 4. Comments and Supplements 435
§ 5. Exercises
Chapter 15
Harmonic Analysis on Homogeneous Spaces
§ 1. Invariant Operators on Homogeneous Spaces 439
§ 2. Harmonic Analysis on Homogeneous Spaces 441
§ 3. Harmonic Analysis on Symmetric Spaces Associated with Pseudo
Orthogonal Groups SO(p, q) 446
§ 4. Generalized Projection Operators 459
§ 5. Comments and Supplements 466
§ 6. Exercises 470
Chapter 16
Induced Representations
§ 1. The Concept of Induced Representations 473
§ 2. Basic Properties of Induced Representation 487
CONTENTS yjjj
§ 3. Systems of Imprimitivity 493
§ 4. Comments and Supplements 501
§ 5. Exercises 493
Chapter 17
Induced Representations of semidirect Products
§ 1. Representation Theory of Semidirect Products 503
§2. Induced Unitary Representations of the Poincare Group 513
§ 3. Representation of the Extended Poincare Group 525
§ 4. Indecomposable Representations of Poincare Group 527
§ 5. Comments and Supplements 536
§ 6. Exercises 537
Chapter 18
Fundamental Theorems of Induced Representations
§ 1. The Induction Reduction Theorem 540
§ 2. Tensor Product Theorem 546
§ 3. The Frobenius Reciprocity Theorem 549
§ 4. Comments and Supplements 553
§ 5. Exercises 553
Chapter 19
Induced Representations of Semisimple Lie Groups
§ 1. Induced Representations of Semisimple Lie Groups 555
§ 2. Properties of the Group SL(w, C) and Its Subgroups 559
§ 3. The Principal Nondegenerate Series of Unitary Representations of
SLO, C) 560
§ 4. Principal Degenerate Series of SL(/?, C) 567
§ 5. Supplementary Nondegenerate and Degenerate Series 570
§ 6. Comments and Supplements 577
§ 7. Exercises 578
Chapter 20
Applications of Induced Representations
§ 1. The Relativistic Position Operator 581
§ 2. The Representations of the Heisenberg Commutation Relations . . 588
§ 3. Comments and Supplements 591
§ 4. Exercises 593
Chapter 21
Group Representations in Relativistic Quantum. Theory
§1. Relativistic Wave Equations and Induced Representations .... 596
§ 2. Finite Component Relativistic Wave Equations 601
XIV CONTENTS
§ 3. Infinite Component Wave Equations 609
§ 4. Group Extensions and Applications 619
§ 5. Space Time and Internal Symmetries 626
§ 6. Comments and Supplements 630
§ 7. Exercises 636
Appendix A
Algebra, Topology, Measure and Integration Theory 637
Appendix B
Functional Analysis
§ 1. Closed, Symmetric and Self Adjoint Operators in Hilbert Space . . 641
§ 2. Integration of Vector and Operator Functions 645
§ 3. Spectral Theory of Operators 649
§ 4. Functions of Self Adjoint Operators 662
§ 5. Essentially Self Adjoint Operators 663
Bibliography 667
List of Important Symbols 703
Author Index 706
Subject Index 710
|
| any_adam_object | 1 |
| author | Barut, Asim O. 1926-1994 Rączka, Ryszard 1931-1996 |
| author_GND | (DE-588)143274074 (DE-588)1053302282 |
| author_facet | Barut, Asim O. 1926-1994 Rączka, Ryszard 1931-1996 |
| author_role | aut aut |
| author_sort | Barut, Asim O. 1926-1994 |
| author_variant | a o b ao aob r r rr |
| building | Verbundindex |
| bvnumber | BV003635732 |
| classification_rvk | SK 260 UK 3000 |
| ctrlnum | (OCoLC)168932416 (DE-599)BVBBV003635732 |
| discipline | Physik Mathematik |
| edition | 2. rev. ed. |
| format | Book |
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| id | DE-604.BV003635732 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T08:07:48Z |
| institution | BVB |
| isbn | 8301027169 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002316289 |
| oclc_num | 168932416 |
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| owner_facet | DE-384 DE-703 DE-355 DE-BY-UBR DE-824 DE-29T DE-19 DE-BY-UBM DE-83 |
| physical | XIX, 717 S. |
| publishDate | 1980 |
| publishDateSearch | 1980 |
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| publisher | Polish Scientific Publ. |
| record_format | marc |
| spellingShingle | Barut, Asim O. 1926-1994 Rączka, Ryszard 1931-1996 Theory of group representations and applications Fizyka matematyczna jhpk Reprezentacje grup jhpk Anwendung (DE-588)4196864-5 gnd Gruppentheorie (DE-588)4072157-7 gnd Gruppe Mathematik (DE-588)4022379-6 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| subject_GND | (DE-588)4196864-5 (DE-588)4072157-7 (DE-588)4022379-6 (DE-588)4128289-9 (DE-588)4148816-7 |
| title | Theory of group representations and applications |
| title_auth | Theory of group representations and applications |
| title_exact_search | Theory of group representations and applications |
| title_full | Theory of group representations and applications Asim O. Barut ; Ryszard Raczka |
| title_fullStr | Theory of group representations and applications Asim O. Barut ; Ryszard Raczka |
| title_full_unstemmed | Theory of group representations and applications Asim O. Barut ; Ryszard Raczka |
| title_short | Theory of group representations and applications |
| title_sort | theory of group representations and applications |
| topic | Fizyka matematyczna jhpk Reprezentacje grup jhpk Anwendung (DE-588)4196864-5 gnd Gruppentheorie (DE-588)4072157-7 gnd Gruppe Mathematik (DE-588)4022379-6 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| topic_facet | Fizyka matematyczna Reprezentacje grup Anwendung Gruppentheorie Gruppe Mathematik Darstellung Mathematik Darstellungstheorie |
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